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Öğe The de Rham Cohomology Classes of Hemi-Slant Submanifolds in Locally Product Riemannian Manifolds(Mdpi, 2024) Gok, Mustafa; Kilic, ErolThis 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.Öğe f(a,b) (3,2,1)-structures on manifolds(Elsevier, 2021) Gok, Mustafa; Kilic, Erol; Ozgur, CihanIn 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.Öğe INVARIANT SUBMANIFOLDS IN GOLDEN RIEMANNIAN MANIFOLDS(Ankara Univ, Fac Sci, 2020) Gok, Mustafa; Keles, Sadik; Kilic, ErolIn 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.Öğe Non-invariant submanifolds of locally decomposable golden Riemannian manifolds(Springer Heidelberg, 2021) Gok, Mustafa; Kilic, ErolIn this paper, we investigate any non-invariant submanifold of a locally decomposable golden Riemannian manifold in the case that the rank of the set of tangent vector fields of the induced structure on the submanifold by the golden structure of the ambient manifold is less than or equal to the codimension of the submanifold.Öğe The relation between the excised thyroid gland weight and postoperative complications in total thyroidectomy patients(2019) Lale, Azmi; Oz, Abdullah Bahadir; Akcan, Alper Celal; Sozuer, Erdogan Mutevelli; Arikan, Turkmen Bahadir; Gok, MustafaAim: The purpose of this study was to determine the postoperative complications in total thyroidectomy patients based on the weight of the thyroid gland with retrospective screening.Material and Methods: A total of 263 adult patients, who underwent total thyroidectomy were included. The data automation system of the hospital and the files of the patients were examined retrospectively.Results: The total complication incidence was 24.3%, and these were determined as hypocalcemia, vocal cord paralyses (VCP), and hemorrhage and seroma at the surgery area. The rate of temporary hypocalcemia and permanent hypocalcemia rate was 20.1% and 1.5% respectively. The temporary VCP rate was 0.3% (n=1), and no permanent VCP was observed in the patients. The median thyroid weight was measured as 50 gr in patients without postoperative hypocalcemia, and as 40 g in the patients with hypocalcemia (p=0.283). There was no significant relation between the variability in the weight of the thyroid and postoperative hypocalcemia. However, the cervical lymph node dissection (LND) (p=0.006) and cervical dissection site (p=0.031) were significant in terms of postoperative complication development. In the multivariate analyses, it was found that female gender and LND were independent risk factors in the development of postoperative complications.Conclusion: It was determined that cervical LND and female gender were independent risk factors. Consistent with the literature findings, no significant results were found in the risk factors like heavy thyroid gland, presence of thyroid operation history, malignant thyroid pathology, retrosternal localization of the thyroid tissue, and hyperthyroidism.Keywords: Complications; hypocalcemia; thyroid weight; total thyroidectomy. Aim: The purpose of this study was to determine the postoperative complications in total thyroidectomy patients based on the weight of the thyroid gland with retrospective screening.Material and Methods: A total of 263 adult patients, who underwent total thyroidectomy were included. The data automation system of the hospital and the files of the patients were examined retrospectively.Results: The total complication incidence was 24.3%, and these were determined as hypocalcemia, vocal cord paralyses (VCP), and hemorrhage and seroma at the surgery area. The rate of temporary hypocalcemia and permanent hypocalcemia rate was 20.1% and 1.5% respectively. The temporary VCP rate was 0.3% (n=1), and no permanent VCP was observed in the patients. The median thyroid weight was measured as 50 gr in patients without postoperative hypocalcemia, and as 40 g in the patients with hypocalcemia (p=0.283). There was no significant relation between the variability in the weight of the thyroid and postoperative hypocalcemia. However, the cervical lymph node dissection (LND) (p=0.006) and cervical dissection site (p=0.031) were significant in terms of postoperative complication development. In the multivariate analyses, it was found that female gender and LND were independent risk factors in the development of postoperative complications.Conclusion: It was determined that cervical LND and female gender were independent risk factors. Consistent with the literature findings, no significant results were found in the risk factors like heavy thyroid gland, presence of thyroid operation history, malignant thyroid pathology, retrosternal localization of the thyroid tissue, and hyperthyroidism.Keywords: Complications; hypocalcemia; thyroid weight; total thyroidectomy.Öğe Reliability of testicular stiffness measurement by shear wave elastography to predict testicular atrophy in patients with chronic liver disease(2020) Sahin, Tuna; Ertekin, Ersen; Gok, Mustafa; Kandemir, Altay; Ture, MevlutAim: Chronic liver disease is one of the most important public health problems in both developed and developing countries. It has been reported that testicular atrophy may occur in these patients. The aim of this study is to demonstrate changes in testicular structure and elasticity due to hypogonadism secondary to chronic liver disease (CLD) by shear wave elastography (SWE).Material and Methods: Eighteen patients aged 22-50 years were included in the study. The control group consisted of 16 participants aged 17-52 years. In all patients and in the control group; first scrotal gray scale and doppler US examination were performed to determine the presence of focal lesions and structural anomalies in both testicles, then the mean testicular shear wave velocity values (SWVV) in the parenchyma was calculated. Testicular volumes and testicular arterial flow indices (Vmax, RI) were recorded. Results: The results of 34 participants (patient and control groups) were examined; There was no significant difference between volumetric measurements, flow indices and SWVQ values between the two groups. In addition, right testicular arterial Vmax values were lower in the patient group than in the control group (p 0.005). Conclusion: A decrease in right testicular arterial Vmax indicates that CLD may play an acceptable role in the development of testicular atrophy. However, the duration of the disease and the drugs used can have an impact on our findings. Prospective studies with larger cohorts may be useful in revealing this relationship.Öğe Schouten and Vranceanu Connections on Golden Manifolds(Int Electronic Journal Geometry, 2019) Gok, Mustafa; Keles, Sadik; Kilic, ErolIn this paper, we study two special linear connections, which are called Schouten and Vranceanu connections, defined by an arbitrary fixed linear connection on a differentiable manifold admitting a golden structure. The golden structure defines two naturally complementary projection operators splitting the tangent bundle into two complementary parts, so there are two globally complementary distributions of the tangent bundle. We examine the conditions of parallelism for both of the distributions with respect to the fixed linear connection under the assumption that it is either the Levi-Civita connection or is not. We investigate the concepts of half parallelism and anti half parallelism for each of the distributions with respect to the Schouten and Vranceanu connections. We research integrability conditions of the golden structure and its associated distributions from the viewpoint of the Schouten and Vranceanu connections. Finally, we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vranceanu connections.Öğe Some Characterizations of Semi-Invariant Submanifolds of Golden Riemannian Manifolds(Mdpi, 2019) Gok, Mustafa; Keles, Sadik; Kilic, ErolIn this paper, we study some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant in terms of canonical structures on the submanifold, induced by the golden structure of the ambient manifold. Besides, we determine forms of the distributions involved in the characterizations of a semi-invariant submanifold on both its tangent and normal bundles.Öğe The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds(Int Electronic Journal Geometry, 2023) Gok, Mustafa; Kilic, ErolIn this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.Öğe Totally Umbilical Semi-Invariant Submanifolds in Locally Decomposable Metallic Riemannian Manifolds(Univ Nis, Fac Sci Math, 2022) Gok, Mustafa; Kilic, ErolIn this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no totally umbilical proper semi-invariant submanifolds in a posivitely or negatively curved locally decomposable metallic Riemannian manifold.
