scholarly journals Some Results on Super Quasi-Einstein Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shyamal Kumar Hui ◽  
Richard S. Lemence
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifolds ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

This paper deals with the study of super quasi-Einstein manifolds admitting -curvature tensor. The totally umbilical hypersurfaces of are also studied. Among others, the existence of such a manifold is ensured by a nontrivial example.

scholarly journals Totally umbilical hypersurfaces of a locally product Riemannian manifold

1967 ◽  
Vol 19 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Masafumi Okumura
Keyword(s):  
Riemannian Manifold ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

scholarly journals Characterization of totally umbilical hypersurfaces

1981 ◽  
Vol 81 (3) ◽  
pp. 447-447 ◽  
Author(s):  
Thomas Hasanis
Keyword(s):  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

scholarly journals Totally umbilical hypersurfaces of manifolds admitting a unit Killing field

2012 ◽  
Vol 364 (7) ◽  
pp. 3609-3626 ◽  
Author(s):  
Rabah Souam ◽  
Joeri Van der Veken
Keyword(s):  
Killing Field ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

Family of Totally Umbilical Hypersurfaces in an Einstein Space

1943 ◽  
Vol 44 (2) ◽  
pp. 271 ◽  
Author(s):  
Yung-Chow Wong
Keyword(s):  
Einstein Space ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

A characterization of totally umbilical hypersurfaces in de Sitter space

2004 ◽  
Vol 51 (1) ◽  
pp. 34-39 ◽  
Author(s):  
Sung-Eun Koh ◽  
Myung-Suk Yoo
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

Some curvature restricted geometric structures for projective curvature tensors

2018 ◽  
Vol 15 (09) ◽  
pp. 1850157 ◽  
Author(s):  
Absos Ali Shaikh ◽  
Haradhan Kundu
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifolds ◽  
Geometric Structures ◽  
Projective Curvature ◽  
Riemannian Case ◽  
Projective Curvature Tensor ◽  
Projective Operator ◽  
Curvature Tensors

The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is shown that the geometric structures formed by imposing projective operator on a (0,4)-tensor is different from that for the corresponding (1,3)-tensor. Characterization of various semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor are obtained on semi-Riemannian manifolds, and it is shown that some of them reduce to Einstein manifolds for the Riemannian case. Finally, to support our theorems, four suitable examples are presented.

ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

2016 ◽  
Vol 103 (1) ◽  
pp. 45-58
Author(s):  
C. P. AQUINO ◽  
M. BATISTA ◽  
H. F. DE LIMA
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Warped Product ◽  
Gauss Map ◽  
Higher Order ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces ◽  
Product Models ◽  
Higher Order Mean Curvature ◽  
Complete Hypersurfaces

In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature. Furthermore, working with different warped product models for$\mathbb{H}^{n+1}$and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in$\mathbb{H}^{n+1}$.

scholarly journals Totally umbilical hypersurfaces of product spaces

2021 ◽  
Author(s):  
Ronaldo F. de Lima ◽  
João Paulo dos Santos
Keyword(s):  
Product Spaces ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

scholarly journals A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping

2013 ◽  
Vol 65 (4) ◽  
pp. 643-648
Author(s):  
E. Ö. Canfes ◽  
A. Özdeğer
Keyword(s):  
Space Form ◽  
Geodesic Mapping ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

scholarly journals On some classes of generalized quasi Einstein manifolds

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 443-456 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Sufficient Conditions ◽  
Riemannian Curvature ◽  
Einstein Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Concircular Curvature Tensor

In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions R?S = 0,R?S = LSQ(g,S), C?S = 0,?C?S = 0,?W?S = 0 and W2?S = 0 where R, S, C,?C,?W and W2 respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor, concircular curvature tensor, quasi conformal curvature tensor and W2-curvature tensor. Later, we find some sufficient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivial example.

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