On pseudo-umbilical spacelike submanifolds in indefinite space form $$\mathcal {M}_p^{n+p}(c)$$

2021 ◽  
Author(s):  
Majid Ali Choudhary
Keyword(s):  
Space Form ◽  
Spacelike Submanifolds

scholarly journals Willmore spacelike submanifolds in an indefinite space form Nn+p q(c)

2017 ◽  
Vol 102 (116) ◽  
pp. 175-193
Author(s):  
Shichang Shu ◽  
Junfeng Chen
Keyword(s):  
Space Form ◽  
Second Fundamental Form ◽  
Integral Inequalities ◽  
Willmore Functional ◽  
Lorentzian Space ◽  
The Second Fundamental Form ◽  
Spacelike Submanifold ◽  
Spacelike Submanifolds ◽  
The Mean ◽  
Rigidity Theorems

Let Nn+p q(c) be an (n+p)-dimensional connected indefinite space form of index q(1 ? q ? p) and of constant curvature c. Denote by ? : M ? Nn+p q (c) the n-dimensional spacelike submanifold in Nn+p q (c), ? : M ? Nn+p q(c) is called a Willmore spacelike submanifold in Nn+p q(c) if it is a critical submanifold to the Willmore functional W(?) = ?q M ?n dv =?M (S-nH2)n/2 dv, where S and H denote the norm square of the second fundamental form and the mean curvature of M and ?2 = S ? nH2. If q = p, in [14], we proved some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in a Lorentzian space form Nn+p q(c). In this paper, we continue to study this topic and prove some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in an indefinite space form Nn+p q(c) (1 ? q ? p).

scholarly journals Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1399
Author(s):  
Bang-Yen Chen ◽  
Simona Decu ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Space Forms ◽  
Statistical Manifolds ◽  
Spacelike Submanifolds ◽  
Totally Real ◽  
Casorati Curvature

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

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