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Öğe ANTI-INVARIANT ??-COSYMPLECTIC-LIKE STATISTICAL SUBMERSIONS(Vinca Inst Nuclear Sci, 2022) Kazan, SemaOur purpose in this article is to study anti-invariant xi(perpendicular to)-cosymplectic-like statistical submersions from cosymplectic-like statistical manifolds and an example. Also, we investigate the integrability and the totally geodesicness of the distributions and the geometry of foliations.Öğe Anti-invariant Holomorphic Statistical Submersions(Springer Basel Ag, 2023) Kazan, Sema; Takano, KazuhikoOur purpose in this article is to study anti-invariant statistical submersions from holomorphic statistical manifolds. Firstly we introduce holomorphic statistical submersions satisfying the certain condition, after we give anti-invariant statistical submersions satisfying the certain condition. And we supported our results with examples.Öğe Helix Surfaces in Euclidean 3-Space with Density(2021) Kazan, Ahmet; Kazan, SemaThe differential geometry of helix curves and helix hypersurfaces in different spaces has important application areas in many disciplines. Also, the notion of weighted manifold is become to be a very popular topic for scientists in recent years. In this context, after defining the notions of weighted mean curvature (or ??-mean curvature) and weighted Gaussian curvature (or ??-Gaussian curvature) of an n-dimensional hypersurface on manifolds with density, lots of studies have been done by differential geometers in different spaces with different densities. So, in the present study, firstly we give the normal vector field, mean curvature and Gaussian curvature of a helix surface in three dimensional Euclidean space and after that, we obtain the weighted mean curvature and weighted Gaussian curvature of a helix surface generated by a unit speed planar curve in three dimensional Euclidean space with different three densities by stating the parametric equation of this surface. However, we know that a hypersurface is weighted minimal and weighted flat in Eucilidean 3-space with density if the weighted mean curvature and the weighted Gaussian curvature vanish, respectively. So, by using these definitions, we obtain the weighted minimal helix surfaces for these different densities and give some results for weighted flatness of the helix surfaces in Euclidean 3-space. We hope that, this study will bring a new viewpoint to differential geometers who are dealing with constant angle surfaces and in near future, one can handle these surfaces in different spaces with another densities.Öğe On the Characterizations of Convolution Manifolds Obtained by Helix Hypersurfaces(2020) Kazan, SemaAbstract: In this study, a submanifold obtained by tensor product of the immersions of two helix hypersurfaces obtained by planar curves is constructed. It is seen that, this submanifold is a convolution manifold with convolution metric and its minimality is examined. After, some characterizations are given by looking at the totally geodesic of same submanifold.Öğe Pseudosimetrik lightlike hiperyüzeyler(İnönü Üniversitesi, 2014) Kazan, SemaBu tez dört bölümden oluşmaktadır. İlk bölümde problemin ortaya cıkışı, geometrik anlamı ve ilgili calışmalar tanıtılmaktadır. İkinci bölümde, tezin orijinal bölümlerinde kullanılacak tanım ve teoremler verilmektedir. Üçüncü bölüm tezin orijinal bölümlerinden birini oluşturmaktadır. Bu bölümde, bir semi-Riemann manifoldun pseudosimetrik lightlike hiperyüzeyi incelenmektedir. Öncelikle, pseudosimetrik lightlike hiperyüzeylere bir örnek verilmekte ve yeter şartlar sunulmaktadır. Ayrıca, bir lightlike hiperyüzeyin pseudoparalellik durumu incelenmekte ve karakterizasyonlar verilmektedir. Bu bölümde son olarak, bir lightlike hiperyüzeyin Ricci-pseudosimetrik olma şartları da elde edilmekte ve genelleştirilmiş Ricci pseudoparalel lightlike hiperyüzeyler incelenmektedir. Son bölümde ise bir Sasakiyan uzay formun bir lightlike hipery uzeyinin pseudosimetri olma durumu incelenerek çeşitli karakterizasyonlar elde edilmektedir. Ayrıca, bir Sasakiyan uzay formun bir lightlike hiperyüzeyinin pseudoparalelliği çalışılmakta ve karakterizasyonlar verilmektedir. Daha sonra, bir Sasakiyan uzay formun bir lightlike hipery uzeyinin Ricci-pseudosimetri şartı incelenmektedir. Son olarak da, bir Sasakiyan uzay formun bir lightlike hiperyüzeyinin Weyl projektif pseudosimetrikliği tanımlanarak bazı sonuçlar verilmektedir.Öğe Pseudosymmetric lightlike hypersurfaces(Tubitak Scientific & Technological Research Council Turkey, 2014) Kazan, Sema; Sahin, BayramWe study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.Öğe PSEUDOSYMMETRIC LIGHTLIKE HYPERSURFACES IN INDEFINITE SASAKIAN SPACE FORMS(Wilmington Scientific Publisher, Llc, 2016) Kazan, Sema; Sahin, BayramWe study pseudosymmetric lightlike hypersurfaces of an indefinite Sasakian space form, tangent to the structure vector field. We obtain sufficient conditions for a lightlike hypersurface to be pseudosymmetric, pseudoparallel and Ricci-pseudosymmetric in an indefinite Sasakian space form. We also find certain conditions for a pseudosymmetric lightlike hypersurface of an indefinite Sasakian space form to be totally geodesic and check the effect of Weyl projective pseudosymmetry conditions on the geometry of a lightlike hyper surface of an indefinite Sasakian space form. Moreover we give some physical interpretations of pseudo-symmetry conditions.Öğe SASAKIAN STATISTICAL MANIFOLDS WITH QSM-CONNECTION AND THEIR SUBMANIFOLDS(Honam Mathematical Soc, 2023) Kazan, SemaIn this present paper, we study QSM-connection (quarter symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection V similar to and the torsion free connection V and obtain the relation between the curvature tensors R similar to of similar to similar to the dual connection V* of V. Also, we give the relations between the curvature tensor R similar to of QSM-connection V similar to and the curvature tensors R and R* of the connections V and V* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection V similar to and the Ricci tensors of the connections V and V*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the sub manifolds with the induced connection with respect to QSM-connection of statistical manifolds. V and R of V. After then we obtain these relations for V andÖğe Screen almost semi-invariant lightlike submanifolds of indefinite Kaehler manifolds(World Scientific Publ Co Pte Ltd, 2024) Kazan, Sema; Yildirim, CumaliIn this paper, we introduce screen almost semi-invariant (SASI)-lightlike submanifolds of indefinite Kaehler manifolds. We obtain the necessary and sufficient condition for the induced connection to be a metric connection on SASI-lightlike submanifolds and construct an example for this manifold. Also, we find some conditions for integrability of distributions and investigate certain characterizations.Öğe Statistical Submersions with Parallel Almost Complex Structures(Springer Basel Ag, 2024) Takano, Kazuhiko; Kazan, SemaThe aim of the present paper is to study statistical submersions with parallel almost complex structures. First, we define the notion of the generalized K & auml;hler-like statistical submersion and give examples of the K & auml;hler-like statistical submersions. In addition, we investigate total space and fibers under certain conditions. After, we introduce some results on J-invariant, J & lowast; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J<^>{*}$$\end{document} -invariant and anti-invariant generalized K & auml;hler-like statistical submersions.
