Three-dimensional locally homogeneous Lorentzian affine hyperspheres with constant sectional curvature

2013 ◽  
Vol 104 (1) ◽  
pp. 137-152 ◽  
Author(s):  
Masahiro Ooguri
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Constant Sectional Curvature ◽  
Locally Homogeneous

scholarly journals Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

scholarly journals On three-dimensional (m,ρ)-quasi-Einstein N(k)-contact metric manifold

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2801-2809
Author(s):  
Avijit Sarkar ◽  
Uday De ◽  
Gour Biswas
Keyword(s):  
Sectional Curvature ◽  
Einstein Manifold ◽  
Three Dimensional ◽  
Constant Sectional Curvature ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds

(m,?)-quasi-Einstein N(k)-contact metric manifolds have been studied and it is established that if such a manifold is a (m,?)-quasi-Einstein manifold, then the manifold is a manifold of constant sectional curvature k. Further analysis has been done for gradient Einstein soliton, in particular. Obtained results are supported by an illustrative example.

Homogeneous Einstein Finsler Metrics on -dimensional Spheres

2018 ◽  
Vol 62 (3) ◽  
pp. 509-523
Author(s):  
Libing Huang ◽  
Xiaohuan Mo
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Einstein Metrics ◽  
Constant Sectional Curvature ◽  
Einstein Metric ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Order Ordinary Differential Equation ◽  
Canonical Metric ◽  
Homogeneous Einstein Metrics

AbstractIn this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

scholarly journals Constant curved minimal CR 3-spheres in CPn

2005 ◽  
Vol 79 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Zhen-Qi Li ◽  
An-Min Huang
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Complex Projective Space ◽  
Constant Sectional Curvature ◽  
Full Dimension ◽  
Analytic Expression ◽  
Complex Projective

AbstractIn this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space CPn are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be c = 1/(m2-1) for some integer m≥ 2, and the full dimension is n = 2m2-3. An explicit analytic expression for such an immersion is given.

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