Yazar "Tripathi, Mukut Mani" seçeneğine göre listele

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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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    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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    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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    ??-submanifolds of para-Sasakian manifolds
    (Tubitak Scientific & Technological Research Council Turkey, 2014) Yuksel Perktas, Selcen; Tripathi, Mukut Mani; Kilic, Erol; Keles, Sadik
    Almost semiinvariant xi(perpendicular to)-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant xi(perpendicular to)-submanifolds and semiinvariant xi(perpendicular to)-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant xi(perpendicular to)-submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-CR-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant xi(perpendicular to)-submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.