Hypersurfaces of the hyperbolic space with constant scalar curvature

2005 ◽  
Vol 48 (1-2) ◽  
pp. 65-88 ◽  
Author(s):  
Zejun Hu ◽  
Shujie Zhai
Keyword(s):  
Scalar Curvature ◽  
Hyperbolic Space ◽  
Constant Scalar Curvature

Hyperbolic submanifolds with finite type hyperbolic Gauss map

2015 ◽  
Vol 26 (02) ◽  
pp. 1550014 ◽  
Author(s):  
Uğur Dursun ◽  
Rüya Yeğin
Keyword(s):  
Scalar Curvature ◽  
Finite Type ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Gauss Map ◽  
Hyperbolic Spaces ◽  
Nonzero Constant ◽  
Hyperbolic Gauss Map

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

An Einstein-like metric on almost Кenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4695-4702 ◽  
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Scalar Curvature ◽  
Hyperbolic Space ◽  
Critical Condition ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Kenmotsu Manifold ◽  
Almost Kenmotsu Manifold

In this paper, we prove that if the metric of a three-dimensional (k,?)'-almost Kenmotsu manifold satisfies the Miao-Tam critical condition, then the manifold is locally isometric to the hyperbolic space H3(-1). Moreover, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the Miao-Tam critical condition, then the manifold is either of constant scalar curvature or Einstein. Some corollaries of main results are also given.

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].

Curvature bounds for the spectrum of a compact Riemannian manifold of constant scalar curvature

2005 ◽  
Vol 15 (4) ◽  
pp. 589-606 ◽  
Author(s):  
Sharief Deshmukh ◽  
Afifah Al-Eid
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Compact Riemannian Manifold ◽  
Constant Scalar Curvature ◽  
Curvature Bounds

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.

Sign in / Sign up

Export Citation Format

Share Document