Browsing by Author "Shanker, Gauree"

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    Constant curvature conditions for generalized kropina spaces
    (RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2021-03-01T00:00:00) Shanker, Gauree; Sharma, Ruchi Kaushik
    The classification of Finsler spaces of constant curvature is an interesting and important topic of research in differential geometry. In this paper we obtain necessary and sucient conditions for generalized Kropina space to be of constant flag curvature. � 2021, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.
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    First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications; [Premi�re in�galit� de Chen pour des produits tordus de sous-vari�t�s d�un espace forme riemannien et applications]
    (ISTE Group, 2023-06-15T00:00:00) Mustafa, Abdulqader; �zel, Cenap; Pigazzini, Alexander; Kaur, Ramandeep; Shanker, Gauree
    In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants (?-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Chen�s Problem 1 relating to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of a submanifold. As a geometric application, this inequality is applied to derive a necessary condition for the immersed submanifold to be minimal in Riemannian space forms, which presents a partial answer for the well-known problem proposed by S.S. Chern, Problem 2. For further research directions, we address a couple of open problems; namely Problem 3 and Problem 4. � 2023 ISTE OpenScience � Published by ISTE Ltd. London, UK.
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    A study on the geometry of totally umbilical (TU) screen-transversal (ST) lightlike submanifolds of metallic semi-Riemannian manifolds
    (American Institute of Physics Inc., 2022-03-19T00:00:00) Shanker, Gauree; Yadav, Ankit
    We scrutinize geometry of TU screen-transversal(ST) lightlike submanifolds. Two classes, TU radical ST lightlike submanifolds and TU ST anti-invariant lightlike submanifolds, are studied. The necessary and sufficient conditions for the distributions to be integrable and the induced connection to be a Levi-Civita or metric connection on these mentioned lightlike submanifolds are derived. Further, some important results are established on the geometry of these submanifolds. This paper contributes various important results that help the further study of the geometry of metallic semi-Riemannian manifolds. � 2022 Author(s).