scholarly journals Some Results on Generalized Quasi-Einstein Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. G. Prakasha ◽  
H. Venkatesha
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
Geometric Properties ◽  
Conharmonic Curvature Tensor

This paper deals with generalized quasi-Einstein manifold satisfying certain conditions on conharmonic curvature tensor. Here we study some geometric properties of generalized quasi-Einstein manifold and obtain results which reveal the nature of its associated 1-forms.

scholarly journals On generalized quasi-Einstein manifolds admitting certain vector fields

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 599-609 ◽  
Author(s):  
Uday De ◽  
Sahanous Mallick
Keyword(s):  
Vector Fields ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
Geometric Properties

The object of the present paper is to study some geometric properties of a generalized quasi-Einstein manifold. The existence of such a manifold have been proved by several non-trivial examples.

scholarly journals On generalized Quasi Einstein manifolds

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 811-820 ◽  
Author(s):  
Avik De ◽  
Ahmet Yildiz ◽  
Uday De
Keyword(s):  
Einstein Manifold ◽  
Natural Generalization ◽  
Einstein Manifolds ◽  
Geometric Properties

Quasi Einstein manifold is a simple and natural generalization of an Einstein manifold. The object of the present paper is to study some geometric properties of generalized quasi Einstein manifolds. Two non-trivial examples have been constructed to prove the existence of a generalized quasi Einstein manifold.

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.

scholarly journals Locally Conformal Almost Cosymplectic Manifold of Φ-holomorphic Sectional Conharmonic Curvature Tensor

2018 ◽  
Vol 11 (3) ◽  
pp. 671-681 ◽  
Author(s):  
Habeeb Mtashar Abood ◽  
Farah Al-Hussaini
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Cosymplectic Manifold ◽  
Almost Cosymplectic Manifold ◽  
Conharmonic Curvature Tensor ◽  
Locally Conformal

The aim of the present paper is to study the geometry of locally conformal almost cosymplectic manifold of Φ-holomorphic sectional conharmonic curvature tensor. In particular, the necessaryand sucient conditions in which that locally conformal almost cosymplectic manifold is a manifold of point constant Φ-holomorphic sectional conharmonic curvature tensor have been found. The relation between the mentioned manifold and the Einstein manifold is determined.

scholarly journals Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 721-731 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Projective Flatness

In this paper we determine some properties of pseudo-projective curvature tensor denoted by ?P on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

Almost pseudo-Q-symmetric semi-Riemannian manifolds

2018 ◽  
Vol 15 (07) ◽  
pp. 1850117
Author(s):  
Ljubica Velimirović ◽  
Pradip Majhi ◽  
Uday Chand De
Keyword(s):  
Perfect Fluid ◽  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Properties ◽  
Dust Fluid ◽  
Necessary And Sufficient ◽  
Fluid Spacetimes

The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider [Formula: see text]-spacetimes.

scholarly journals Stability of Riemannian manifolds with Killing spinors

2017 ◽  
Vol 28 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Changliang Wang
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Stability Result ◽  
Warped Products ◽  
Einstein Manifolds ◽  
Killing Spinors ◽  
Parallel Spinors ◽  
Unstable Manifolds ◽  
The Stability ◽  
Complete Riemannian Manifolds

Riemannian manifolds with nonzero Killing spinors are Einstein manifolds. Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1 ]. In this paper, we obtain a new proof for this stability result by using a Bochner-type formula in [X. Dai, X. Wang and G. Wei, On the stability of Riemannian manifold with parallel spinors, Invent. Math. 161(1) (2005) 151–176; M. Wang, Preserving parallel spinors under metric deformations, Indiana Univ. Math. J. 40 (1991) 815–844]. Moreover, existence of real Killing spinors is closely related to the Sasaki–Einstein structure. A regular Sasaki–Einstein manifold is essentially the total space of a certain principal [Formula: see text]-bundle over a Kähler–Einstein manifold. We prove that if the base space is a product of two Kähler–Einstein manifolds then the regular Sasaki–Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.

scholarly journals ON PSEUDO CYCLIC RICCI SYMMETRIC MANIFOLDS

2009 ◽  
Vol 02 (02) ◽  
pp. 227-237
Author(s):  
Absos Ali Shaikh ◽  
Shyamal Kumar Hui
Keyword(s):  
Riemannian Manifold ◽  
Einstein Manifold ◽  
Conformally Flat ◽  
Geometric Properties ◽  
Symmetric Manifold ◽  
Euclidean Manifold ◽  
Flat Riemannian Manifold

The object of the present paper is to introduce a type of non-flat Riemannian manifold called pseudo cyclic Ricci symmetric manifold and study its geometric properties. Among others it is shown that a pseudo cyclic Ricci symmetric manifold is a special type of quasi-Einstein manifold. In this paper we also study conformally flat pseudo cyclic Ricci symmetric manifolds and prove that such a manifold can be isometrically immersed in a Euclidean manifold as a hypersurface.

scholarly journals On some classes of mixed-super quasi-Einstein manifolds

2016 ◽  
Vol 8 (1) ◽  
pp. 32-52
Author(s):  
Santu Dey ◽  
Buddhadev Pal ◽  
Arindam Bhattacharyya
Keyword(s):  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Einstein Manifolds

Abstract Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

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