Recent Developments in Wintgen Inequality and Wintgen Ideal Submanifolds
Bang-Yen Chen
- Vol. 14, Iss: 1, pp 6-45
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The article was published on 2021-03-17 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Ideal (set theory).read more
Citations
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A classification of Roter type spacetimes
TL;DR: In this article, an algebraic classification of the Roter type spacetimes is given, and it is shown that the curvature condition is essentially equivalent with the pseudosymmetry condition on 4-spacetimes.
Journal ArticleDOI
Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms
Simona Decu,Stefan Haesen +1 more
TL;DR: In this paper , the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms are proved.
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A Note on Some Generalized Curvature Tensor
Ryszard Deszcz,Małgorzata Głogowska,Marian Hotlo's,Miroslava Petrovi'c-Torgavsev,Georges Zafindratafa +4 more
TL;DR: In this article , a generalized curvature tensor E is defined as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold.
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Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms.
TL;DR: In this paper, the authors established some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvatures of totally real spacelike submanifolds in statistical manifolds of the type para-Kahler space form.
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Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds
TL;DR: In this paper , a class of optimum inequalities for submanifolds in Kenmotsu-like statistical manifolds containing the normalized scalar curvature and the generalized normalized Casorati curvatures is presented.
References
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Book
Handbook of elliptic integrals for engineers and scientists
Paul F. Byrd,Morris D. Friedman +1 more
TL;DR: The Handbook of Elliptic Integrals for Engineers and Scientists introduces an integral operator on the set of means and investigates its properties.
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Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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Some pinching and classification theorems for minimal submanifolds
TL;DR: In this paper, the authors define an immersion from an n-dimensional (n > 0) mani- fold into a Euclidean re, space and define the Laplacian operator of M with respect to the induced metric.