scholarly journals On biconservative hypersurfaces in pseudo-Riemannian space forms and their Gauss map

2018 ◽  
Vol 103 (117) ◽  
pp. 223-236 ◽  
Author(s):  
Nurettin Turgay
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Space Form ◽  
Gauss Map ◽  
Space Forms ◽  
Geometrical Properties ◽  
Riemannian Space Forms ◽  
Biconservative Hypersurfaces

We first present a survey about recent results on biconservative hypersurfaces in the Minkowski space E4 1, pseudo-Euclidean space E5 2 and Rieamnnian space-form H4. Then we obtain some geometrical properties of these hypersurface families concerning their mean curvature and Gauss map.

scholarly journals Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Chao Yang ◽  
Jiancheng Liu
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal.

Biharmonic hypersurfaces in pseudo-Riemannian space forms

2016 ◽  
Vol 13 (07) ◽  
pp. 1650094 ◽  
Author(s):  
Dan Yang ◽  
Yu Fu
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
Constant Sectional Curvature ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

Let [Formula: see text] be a nondegenerate biharmonic pseudo-Riemannian hypersurface in a pseudo-Riemannian space form [Formula: see text] with constant sectional curvature [Formula: see text]. We show that [Formula: see text] has constant mean curvature provided that it has three distinct principal curvatures and the Weingarten operator can be diagonalizable.

scholarly journals B.-Y. Chen inequalities for semislant submanifolds in Sasakian space forms

2003 ◽  
Vol 2003 (27) ◽  
pp. 1731-1738 ◽  
Author(s):  
Dragoş Cioroboiu
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Sasakian Manifold ◽  
Sharp Inequality ◽  
Space Forms ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Sasakian Space Forms ◽  
Riemannian Space Forms

Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. The notion of a semislant submanifold of a Sasakian manifold was introduced by J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez (1999). In the present paper, we establish Chen inequalities for semislant submanifolds in Sasakian space forms by using subspaces orthogonal to the Reeb vector fieldξ.

scholarly journals Ricci curvature of submanifolds in Sasakian space forms

2002 ◽  
Vol 72 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Ion Mihai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Arbitrary Codimension ◽  
Complex Space Forms

AbstractRecently, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Afterwards, we dealt with similar problems for submanifolds in complex space forms.In the present paper, we obtain sharp inequalities between the Ricci curvature and the squared mean curvature for submanifolds in Sasakian space forms. Also, estimates of the scalar curvature and the k-Ricci curvature respectively, in terms of the squared mean curvature, are proved.

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