Yazar "Kilic, Erol" seçeneğine göre listele

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    Almost bi-slant submanifolds of an almost contact metric manifold
    (Springer Basel Ag, 2021) Perktas, Selcen Yuksel; Blaga, Adara M.; Kilic, Erol
    In this paper we introduce and study the almost bi-slant submanifolds of an almost contact metric manifold. We give some characterization theorems for almost bi-slant submanifolds. Moreover, we obtain integrability conditions of the distributions which are involved in the definition of almost bi-slant submanifolds. We also get some results for totally geodesic and totally umbilical almost bi-slant submanifolds of cosymplectic manifolds and Sasakian manifolds.
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    Biharmonic Curves in Lorentzian Para-Sasakian Manifolds
    (Malaysian Mathematical Sciences Soc, 2010) Keles, Sadik; Perktas, Selcen Yueksel; Kilic, Erol
    In this paper we give necessary and sufficient conditions for space-like and timelike curves in a conformally fiat, quasi conformally flat and conformally symmetric 4-dimensional Lorentzian Para-Sasakian (LP-Sasakian) manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere S-1(4).
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    BIHARMONIC HYPERSURFACES OF LP-SASAKIAN MANIFOLDS
    (Alexandru Ioan Cuza Univ Press, Alexandru Ioan Cuza Univ Iasi, 2011) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent hyperplane of the hypersurface. We find some necessary and sufficient conditions for a timelike hypersurface of a Lorentzian para-Sasakian manifold to be proper biharmonic. The nonexistence of proper biharmonic timelike hypersurfaces with constant mean curvature in a Ricci flat Lorentzian para-Sasakian manifold is proved.
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    Biharmonic maps between doubly warped product manifolds
    (Balkan Soc Geometers, 2010) Perktas, Selcen Yueksel; Kilic, Erol
    In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds Band F into the nontrivial (proper) doubly warped product manifold (f)B x(b) F cannot be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections (f)B x(b) F -> B and (f)B x(b) F -> F, respectively. Some characterizations for non-harmonic biharmonic maps are given by using product of harmonic maps and warping metric. Especially, in the case of f = 1, the results for warped product in [4] are obtained.
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    Bochner-Chen Ideal Submanifolds
    (Chiang Mai Univ, Fac Science, 2020) Kilic, Erol; Gulbahar, Mehmet
    In this paper, we investigate ideal invariant submanifolds, ideal anti-invariant submanifolds and ideal CR-submanifolds of Bochner Kaehler manifolds. Moreover, some characterizations related with the holomorphic sectional curvature and the anti-holomorphic sectional curvature are obtained for Bochner Kaehler manifolds.
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    Can postoperative atelectasis be prevented by local bupivacaine infusion/infiltration after emergency upper midline laparotomy? Randomized clinical trial
    (2019) Kilic, Erol; Ugur, Mustafa
    Aim: To investigate the effectivity of conventional analgesia and transfascial local bupivacaine infusion used for postoperative pain management on the development of postoperative atelectasisin patients undergoing upper abdominal surgery by midline laparotomy.Materials and Methods: The prospective study included patients that underwent emergency UAS by midline laparotomy and were administered conventional analgesia (CA) (nonsteroidal anti-inflammatory drugs [NSAIDs] + opioids) or transfascial bupivacaine infusion (TBI) (NSAIDs + bupivacaine) following extubating.Results: The groups were similar with regard to age, preoperative ASA status, surgical indications, and operative time (p>0.05). Mean Visual Analogue Scale scores at 0-8, 08-24, and 24-48 h and the requirement of opioids were lower in the TBI group compared to the CA group (p0.05). The median length of intensive care unit stay was significantly lower in the TBI group compared to the CA group (4 and 5 days, respectively) (p0.05).Conclusion: Transfascial bupivacaine infusion/infiltration is effective not only in providing postoperative analgesia but also in the prevention of postoperative atelectasis.Keywords: Transfascial bupivacaine infusion, postoperative atelectasis, postoperative analgesia.
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    CHEN INVARIANTS FOR RIEMANNIAN SUBMERSIONS AND THEIR APPLICATIONS
    (Ankara Univ, Fac Sci, 2022) Gulbahar, Mehmet; Meric, Semsi E. K. E. N.; Kilic, Erol
    In this paper, an optimal inequality involving the delta curvature is exposed. With the help of this inequality some characterizations about the vertical motion and the horizontal divergence are obtained.
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    Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds
    (Polish Acad Sciences Inst Mathematics-Impan, 2016) Kilic, Erol; Tripathi, Mukut Mani; Guelbahar, Mehmet
    Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost constant curvature are established. Chen Ricci inequalities for different kinds of submanifolds of Kaehlerian product manifolds are also given.
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    Concurrent Vector Fields on Lightlike Hypersurfaces
    (Mdpi, 2021) Kilic, Erol; Gulbahar, Mehmet; Kavuk, Ecem
    Concurrent vector fields lying on lightlike hypersurfaces of a Lorentzian manifold are investigated. Obtained results dealing with concurrent vector fields are discussed for totally umbilical lightlike hypersurfaces and totally geodesic lightlike hypersurfaces. Furthermore, Ricci soliton lightlike hypersurfaces admitting concurrent vector fields are studied and some characterizations for this frame of hypersurfaces are obtained.
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    Contact-Complex Riemannian Submersions
    (Mdpi, 2021) Bejan, Cornelia-Livia; Meric, Semsi Eken; Kilic, Erol
    A submersion from an almost contact Riemannian manifold to an almost Hermitian manifold, acting on the horizontal distribution by preserving both the metric and the structure, is, roughly speaking a contact-complex Riemannian submersion. This paper deals mainly with a contact-complex Riemannian submersion from an eta-Ricci soliton; it studies when the base manifold is Einstein on one side and when the fibres are eta-Einstein submanifolds on the other side. Some results concerning the potential are also obtained here.
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    The de Rham Cohomology Classes of Hemi-Slant Submanifolds in Locally Product Riemannian Manifolds
    (Mdpi, 2024) Gok, Mustafa; Kilic, Erol
    This paper aims to discuss the de Rham cohomology of hemi-slant submanifolds in locally product Riemannian manifolds. The integrability and geodesical invariance conditions of the distributions derived from the definition of a hemi-slant submanifold are given. The existence and non-triviality of de Rham cohomology classes of hemi-slant submanifolds are investigated. Finally, an example is presented.
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    Effects of surgical and percutaneous tracheotomy on thyroid hormones
    (Edizioni Luigi Pozzi, 2019) Yetim, Tulin Durgun; Ozer, Gul Soylu; Karaaslan, Kerem; Yetim, Brahim; Kilic, Erol
    Aim: To evaluate the effects of surgical and percutaneous tracheotomy on thyroid hormones. MATERIAL AND METHOD: Sixty patients with respiratory problems who underwent surgical tracheotomy and percutaneous tracheotomy between December 2012 and December 2016 were divided into 2 groups. FT3, FT4, thyroglobulin and TSH levels of the groups were statistically evaluated preoperatively and postoperatively. RESULTS: The effects of surgical and percutaneous tracheotomy on free thyroxin (FT4), serum thyroglobulin (TG) and thyroid stimulating hormone (TSH) levels were found to be statistically significant. Although free triiodothyronine (FT3) slightly elevated in both groups, it was not statistically significant. DISCUSSION: Today, percutaneous tracheotomy (PCT) and conventional surgical tracheotomy (CT) have been widely used in intensive care units on patients who are expected to be connected to mechanical ventilation for a long time. Because of the anatomy of the surgical site, tracheotomy may cause damage to the adjacent thyroid gland and tracheal rings CONCLUSION: Surgeons should keep in mind that serum thyroid hormone levels may increase postoperatively. Particularly the patients with cardiac rhythm problems should be followed after surgical and percutaneous tracheotomy due to the systemic effects of thyroid hormones.
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    Einstein like (?)-para Sasakian manifolds
    (Academic Publication Council, 2013) Keles, Sadik; Kilic, Erol; Tripathi, Mukut Mani; Perktas, Selcen Yuksel
    Einstein like (epsilon)-para Sasakian manifolds are introduced. For an (epsilon)-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like (epsilon)-para Sasakian manifold is obtained and it is shown that the scalar curvature in this case must satisfy certain differential equation. A necessary and sufficient condition for an (epsilon)-almost paracontact metric hypersurface of an indefinite locally Riemannian product manifold to be (epsilon)-para Sasakian is obtained and it is proved that the (epsilon)-para Sasakian hypersurface of an indefinite locally Riemannian product manifold of almost constant curvature is always Einstein like.
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    Einstein Metrics Induced by Natural Riemann Extensions
    (Springer Basel Ag, 2017) Bejan, Cornelia-Livia; Meric, Semsi Eken; Kilic, Erol
    Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein's equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225-230, 1999) within a Clifford algebra. Let M be a manifold with a torsion-free connection which induces on its cotangent bundle T* M , a semi-Riemannian metric (g) over bar , called the natural Riemann extension, Kowalski and Sekizawa (Publ Math Debrecen 78:709-721, 2011). The main result of the present paper gives a necessary and sufficient condition for (g) over bar restricted to certain hypersurfaces of T* M to be Einstein.
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    f(a,b) (3,2,1)-structures on manifolds
    (Elsevier, 2021) Gok, Mustafa; Kilic, Erol; Ozgur, Cihan
    In this paper, we define and study two new structures on a differentiable manifold called by us an f((a,b)) (3, 2, 1)-structure and a framed f((a,b)) (3, 2, 1)-structure as a generalization of some geometric structures determined by polynomial structures, where a, b is an element of R and b not equal 0. At beginning, we present some examples regarding f((a,b)) (3, 2,1)-structures and establish their some fundamental properties. We also give a necessary condition for an f((a,b)) (3, 2,1)-structure to be an almost quadratic phi-structure. Later, it is shown that the existence of two semi-Riemannian metrics on differentiable manifolds admitting a framed f((a,b)) (3, 2, 1)-structure, i.e., framed f((a,b)) (3, 2, 1)-manifolds. In particular, a framed f((a,b)) ( 3, 2,1)-manifold endowed with the first semi-Riemannian metric mentioned above is called a framed metric f((a,b)) (3, 2, 1)-manifold. Finally, we construct some examples to illustrate the existence of framed metric f((a,b)) (3, 2, 1)-manifolds. (C) 2021 Elsevier B.V. All rights reserved.
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    HYPERSURFACES OF LORENTZIAN PARA-SASAKIAN MANIFOLDS
    (Matematisk Inst, 2011) Perktas, Selcen Yuksel; Kilic, Erol; Keles, Sadik
    In this paper we study the invariant and noninvariant hypersurfaces of (1, 1, 1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an ( I, 1, 1) almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal (1, 1, 1) almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a non invariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.
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    Ideality of a Coisotropic Lightlike Submanifold
    (Int Electronic Journal Geometry, 2016) Kilic, Erol; Gulbahar, Mehmet
    The notion of best living way on coisotropic lightlike submanifolds is discussed. Some relations involving the screen Ricci curvature and the screen scalar curvature are given. Two examples of coisotropic lightlike submanifolds are mentioned and ideals of leaves of screen distributions in these examples are investigated by the help of these relations.
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    Inequalities for scalar curvature of pseudo-Riemannian submanifolds
    (Elsevier Science Bv, 2017) Tripathi, Mukut Mani; Gulbahar, Mehmet; Kilic, Erol; Keles, Sadik
    Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed. (C) 2016 Elsevier B.V. All rights reserved.
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    INVARIANT SUBMANIFOLDS IN GOLDEN RIEMANNIAN MANIFOLDS
    (Ankara Univ, Fac Sci, 2020) Gok, Mustafa; Keles, Sadik; Kilic, Erol
    In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant sub-manifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any sub-manifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodesicity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.
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    Legendre Curves on Generalized Paracontact Metric Manifolds
    (Springer, 2019) Bejan, Cornelia-Livia; Eken Meric, Semsi; Kilic, Erol
    Two different notions of almost paracontact structures (which are compatible or anti-compatible with the metric), well known in the literature, are unified and generalized here. Several formulas of paraholomorphic maps are established, and a result of Lichnerowicz type is obtained. The connection transformations which have the same system of paracontact-planar Legendre curves are characterized. Conformal changes of metrics which preserve geodesics (resp. paracontact-planar Legendre curves) are studied.