A characterization of Clifford tori with constant scalar curvature one by the first stability eigenvalue

2004 ◽  
Vol 35 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Luis J. Alías ◽  
Aldir Brasil ◽  
Luiz A. M. Sousa
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Clifford Tori ◽  
First Stability Eigenvalue

scholarly journals RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE

2007 ◽  
Vol 49 (2) ◽  
pp. 235-241 ◽  
Author(s):  
GUOXIN WEI ◽  
YOUNG JIN SUH
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Constant Scalar Curvature ◽  
Clifford Tori ◽  
Rigidity Theorems

AbstractIn this paper, we give a characterization of Clifford tori $S^1(\sqrt{\textstyle\frac{nr+2-n}{nr}})\times S^{n-1}(\sqrt{\frac{n-2}{nr}})$ and $S^m(a)\times S^{n-m}(\sqrt{1-a^2}) (2 \le m \le n - 2, 0 \lt a^2 \lt 1)$ in a unit sphere Sn+1 (1). Our results extend the results due to Cheng and Yau [4], and Wang and Xia [11].

scholarly journals Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2362
Author(s):  
Ali H. Alkhaldi ◽  
Pişcoran Laurian-Ioan ◽  
Abimbola Abolarinwa ◽  
Akram Ali
Keyword(s):  
Scalar Curvature ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Constant Scalar Curvature ◽  
Topological Constraints ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Yamabe Solitons

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics.

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.

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