Results 11 to 20 of about 469 (136)
Inequalities for casorati curvatures of submanifolds in real space forms [PDF]
Advances in Geometry, 2016 Abstract Using Oprea’s optimization methods on submanifolds, we give another proof of the inequalities relating the normalized δ-Casoraticurvature δ ^
Zhang, Pan, Zhang, Liang
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Axioms, 2023 In the present article, we consider submanifolds in golden Riemannian manifolds with constant golden sectional curvature. On such submanifolds, we prove geometric inequalities for the Casorati curvatures.
Majid Ali Choudhary, Ion Mihai
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Recent developments in δ-Casorati curvature invariants
TURKISH JOURNAL OF MATHEMATICS, 2021 One of the basic problems in submanifold theory is to find simple relationships between the main extrinsic and intrinsic invariants of a submanifold. In order to obtain viable solutions to this problem, the author introduced in the early 1990's new types of Riemannian invariants, known as \(\delta\)-invariants or Chen invariants.
Bang-Yen Chen
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Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures
Annali di Matematica Pura ed Applicata (1923 -), 2020 The authors consider Riemannian maps and Riemannian submersions to obtain optimal inequalities in the theory of Riemannian maps, Riemannian submersions to space forms. The method is based on Casorati curvature. The important results in this work are described in the following sections: Riemannian maps to real space forms, Riemannian maps to complex ...
Chul Woo Lee +3 more
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Optimal inequalities involving Casorati curvatures for Riemannian maps to nearly Kaehler manifolds
Journal of Inequalities and ApplicationsWe establish a general inequality and optimal inequalities involving the normalized Casorati curvatures and the generalized normalized Casorati curvatures within the horizontal space of a Riemannian map from a Riemannian manifold to a nearly Kaehler ...
Tanveer Fatima +5 more
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Bulletin of the Korean Mathematical Society, 2015 Summary: In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.
Lee, Chul Woo +3 more
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Optimizations on Statistical Hypersurfaces with Casorati Curvatures [PDF]
Kragujevac Journal of Mathematics, 2021 In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δ−Casorati curvatures and also ...
Siddiqui, Aliya Naaz +1 more
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A new proof for some optimal inequalities involving generalized normalized δ-Casorati curvatures [PDF]
Journal of Inequalities and Applications, 2015 Let \(M\) be an \(n\)-dimensional Riemannian submanifold of a Riemannian manifold \((\bar{M},\bar{g})\). Then it is known that the Casorati curvature of \(M\) is an extrinsic invariant defined as the normalized square of the length of the second fundamental form \(h\) of the submanifold (of dimension \(n\)).
Lee, Chul Woo +2 more
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Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds
Mathematics, 2022 In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical ...
Aliya Naaz Siddiqui +2 more
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Tamkang Journal of Mathematics, 2021 The present research article is concerned about a couple of optimal inequalities for submanifolds of $\delta$-Lorentzian trans-Sasakian manifolds endowed with semi-symmetric metric connection (briefly says $SSM$). Some examples of $\delta$-Lorentzian trans-Sasakiam manifolds are also discussed here. This paper ends with some open problems.
Siddiqui, Aliya Naaz +2 more
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