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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Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures
Annali Di Matematica Pura Ed Applicata, 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 ...
Gabriel-Eduard Vilcu +2 more
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Inequalities for the Casorati Curvatures of Real Hypersurfaces in Some Grassmannians
Taiwanese Journal of Mathematics, 2018 In this paper we obtain two types of optimal inequalities consisting of the normalized scalar curvature and the generalized normalized $δ$-Casorati curvatures for real hypersurfaces of complex two-plane Grassmannians and complex hyperbolic two-plane Grassmannians. We also find the conditions on which the equalities hold.
Kwang-Soon Park
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Remarks on inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms [PDF]
Journal of Inequalities and Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Pan, Zhang, Liang
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Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms [PDF]
Journal of Inequalities and Applications, 2014 Abstract In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.
Gabriel-Eduard Vilcu +2 more
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Curvature Bounds and Casorati Pinching for Submanifolds in Kähler Product Manifolds
AxiomsIn this paper, we establish sharp pinching inequalities that relate the generalized δ-Casorati curvatures to the normalized scalar curvature of submanifolds immersed in Kähler product manifolds endowed with a quarter-symmetric metric connection.
Md Aquib +3 more
doaj +2 more sources
A pinching theorem for statistical manifolds with Casorati curvatures
Journal of Nonlinear Science and Applications, 2017 Summary: With a pair of conjugate connections \(\overline{\nabla}\) and \(\overline{\nabla}^*\), we derive optimal Casorati inequalities with the normalized scalar curvature on submanifolds of a statistical manifold of constant curvature.
Jae Won Lee, Chul Woo Lee
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Optimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed with Semi-Symmetric Non-Metric Connections [PDF]
Symmetry, 2016 In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection.
Hairong Liu
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Some Optimal Bounds for δ-Casorati Curvatures with Slant Factor in Trans-Sasakian Manifolds
MathematicsIn this article, we derive some optimal inequalities for slant submanifolds on trans-Sasakian manifolds coupled with quarter-symmetric non-metric connection (qsnmc), utilizing generalized normalized δ-Casorati curvatures.
Rawan Bossly
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