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    Lightlike Submanifolds with Planar Normal Section in Semi Riemannian Product Manifolds
    (Int Electronic Journal Geometry, 2016) Erdogan, Feyza Esra; Yildirim, Cumali
    In the present paper we give conditions for screen semi invariant lightlike submanifolds of a semi-Riemannian product manifold to have degenerate planar normal sections. Also we give sufficient and efficient conditions for screen invariant and screen anti invariant lightlike submanifold of a semi-Riemanniann product manifold to have non-degenerate planar normal sections.
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    On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds
    (Gazi Univ, 2018) Erdogan, Feyza Esra; Yildirim, Cumali
    The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we can say that an (1,1)-tensor field (P) over bar on a m-dimensional Riemann manifold (<(M,<(g)over bar>)over bar>) is a Golden structure if it satisfies the equation (P) over bar (2) = (P) over bar + Id, where Id is identity map on M. Furthermore, g((P) over bar, (X) over bar, (Y) over bar) = (g) over bar((X) over bar,(P) over bar (Y) over bar), the Riemannian metric is called (P) over bar -compatible and ((M) over bar,(g) over bar,(P) over bar) is named a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. For this purpose, we study totally umbilical semi-invariant submanifold of the Golden Riemannian manifolds. Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.
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    ON SEMI-INVARIANT SUBMANIFOLDS OF ALMOST COMPLEX CONTACT METRIC MANIFOLDS
    (Univ Nis, 2016) Yildirim, Cumali; Erdogan, Feyza Esra
    In this article, we study semi-invariant submanifolds of almost complex contact metric manifolds.We defined and investigated semi-invariant submanifolds of almost complex contact metric manifolds. We found necessary and sufficient conditions to be integrable and totally geodesic for distributions D defined on M. Also we obtained necessary and sufficient conditions to be integrable and totally geodesic for distributions D-perpendicular to defined on M.
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    Screen almost semi-invariant lightlike submanifolds of indefinite Kaehler manifolds
    (World Scientific Publ Co Pte Ltd, 2024) Kazan, Sema; Yildirim, Cumali
    In 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.
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    SCREEN TRANSVERSAL LIGHTLIKE SUBMANIFOLDS OF INDEFINITE SASAKIAN MANIFOLDS
    (Sciendo, 2010) Yildirim, Cumali; Sahin, Bayram
    We introduce screen transversal lightlike submanifolds of indefinite almost contact manifolds and show that such submanifolds contain lightlike real curves. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also check the existence of screen transversal lightlike submanifolds in indefinite Sasakian manifolds.
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    Semi-Invariant Submanifolds of Golden Riemannian Manifolds
    (Amer Inst Physics, 2017) Erdogan, Feyza Esra; Yildirim, Cumali
    In this article we studied semi-invariant submanifolds of the Golden Riemannian manifold. We give integrability condition of the distributions and investigate the geometry of foliations. We also find necessary and sufficient conditions for a semi-invariant submanifold to be totally geodesic.
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    Slant lightlike submanifolds of indefinite Sasakian manifolds
    (Univ Nis, Fac Sci Math, 2012) Sahin, Bayram; Yildirim, Cumali
    In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.
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    Transversal lightlike submanifolds of indefinite sasakian manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2010) Yildirim, Cumali; Sahin, Bayram
    We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical transversal lightlike submanifolds