scholarly journals Generalized quasi-Einstein GRW space-times

2019 ◽  
Vol 16 (08) ◽  
pp. 1950124 ◽  
Author(s):  
Uday Chand De ◽  
Sameh Shenawy
Keyword(s):  
Scalar Curvature ◽  
Perfect Fluid ◽  
Constant Scalar Curvature ◽  
Einstein Space

Recently, it is proven that generalized Robertson–Walker space-times in all orthogonal subspaces of Gray’s decomposition except one (unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a constant scalar curvature. It is shown that generalized quasi-Einstein GRW space-times reduce to Einstein space-times or perfect fluid space-times.

Curvature Bounds for the Spectrum of Closed Einstein Spaces

1978 ◽  
Vol 30 (5) ◽  
pp. 1087-1091 ◽  
Author(s):  
Udo Simon
Keyword(s):  
Lower Bound ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Constant Scalar Curvature ◽  
Einstein Space ◽  
Curvature Bounds ◽  
Nonzero Eigenvalue ◽  
Einstein Spaces ◽  
Image Position

The following is our main result.(A) THEOREM. Let (M, g) be a closed connected Einstein space, n = dim M ≧ 2 (with constant scalar curvature R). Let K0 be the lower bound of the sectional curvature. Then either (M, g) is isometrically diffeomorphic to a sphere and the first nonzero eigenvalue ƛ1of the Laplacian fulfils

scholarly journals Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime

2021 ◽  
Author(s):  
Peibiao Zhao ◽  
Uday Chand De ◽  
Bülent Ünal ◽  
Krishnendu De
Keyword(s):  
Cosmological Constant ◽  
Scalar Curvature ◽  
Perfect Fluid ◽  
Sufficient Conditions ◽  
Constant Scalar Curvature ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Dust Fluid ◽  
Perfect Fluid Spacetime

The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein’s field equations without cosmological constant is vacuum. Finally, we construct a nontrivial example of pseudosymmetric spacetime.

Yamabe solitons on 3-dimensional contact metric manifolds with Qφ = φQ

2019 ◽  
Vol 16 (03) ◽  
pp. 1950039 ◽  
Author(s):  
V. Venkatesha ◽  
Devaraja Mallesha Naik
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Contact Metric Manifold ◽  
Reeb Vector Field ◽  
3 Dimensional ◽  
Flow Vector ◽  
Contact Metric Manifolds ◽  
Yamabe Soliton

If [Formula: see text] is a 3-dimensional contact metric manifold such that [Formula: see text] which admits a Yamabe soliton [Formula: see text] with the flow vector field [Formula: see text] pointwise collinear with the Reeb vector field [Formula: see text], then we show that the scalar curvature is constant and the manifold is Sasakian. Moreover, we prove that if [Formula: see text] is endowed with a Yamabe soliton [Formula: see text], then either [Formula: see text] is flat or it has constant scalar curvature and the flow vector field [Formula: see text] is Killing. Furthermore, we show that if [Formula: see text] is non-flat, then either [Formula: see text] is a Sasakian manifold of constant curvature [Formula: see text] or [Formula: see text] is an infinitesimal automorphism of the contact metric structure on [Formula: see text].

Generalized -Einstein Real Hypersurfaces in and

2020 ◽  
Vol 63 (4) ◽  
pp. 909-920
Author(s):  
Yaning Wang
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Coefficient ◽  
Real Hypersurface ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Real Hypersurfaces

AbstractIn this paper we obtain some new characterizations of pseudo-Einstein real hypersurfaces in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$. More precisely, we prove that a real hypersurface in $\mathbb{C}P^{2}$ or $\mathbb{C}H^{2}$ with constant mean curvature is generalized ${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein. We prove that a real hypersurface in $\mathbb{C}P^{2}$ with constant scalar curvature is generalized ${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein.

A Note on Randers Metrics of Scalar Flag Curvature

2012 ◽  
Vol 55 (3) ◽  
pp. 474-486 ◽  
Author(s):  
Bin Chen ◽  
Lili Zhao
Keyword(s):  
Scalar Curvature ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Flag Curvature ◽  
Projectively Flat ◽  
Randers Metrics

AbstractSome families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic S-curvature are given. Certain Randers metrics with Einstein α are considered and proved to be complex. Three dimensional Randers manifolds, with α having constant scalar curvature, are studied.

Spacelike hypersurfaces with constant scalar curvature

1998 ◽  
Vol 95 (4) ◽  
pp. 499-505 ◽  
Author(s):  
Qing-Ming Cheng ◽  
Susumu Ishikawa
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Spacelike Hypersurfaces
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