scholarly journals Extremities for statistical submanifolds in Кenmotsu statistical manifolds

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 591-603
Author(s):  
Aliya Siddiqui ◽  
Young Suh ◽  
Oğuzhan Bahadır
Keyword(s):  
Sectional Curvature ◽  
Contact Geometry ◽  
Optimization Techniques ◽  
Constant Sectional Curvature ◽  
Theoretical Physics ◽  
Statistical Manifold ◽  
Kenmotsu Manifold ◽  
Ricci Flat ◽  
Statistical Manifolds ◽  
Counter Example

Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. It has been shown that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold by constructing a counter-example. Finally, we prove a very well-known Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds of constant ?-sectional curvature by adopting optimization techniques on submanifolds. This article ends with some concluding remarks.

H-curvature tensors on IK-normal complex contact metric manifolds

2018 ◽  
Vol 15 (12) ◽  
pp. 1850205 ◽  
Author(s):  
Aysel Turgut Vanli ◽  
Inan Unal
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Theoretical Physics ◽  
Contact Metric Manifold ◽  
Contact Manifolds ◽  
Normal Complex ◽  
Contact Metric Manifolds ◽  
Curvature Tensors

IK-normal complex contact metric manifolds have some important properties. There are several applications of this kind of contact manifolds in theoretical physics. In this paper, we studied on [Formula: see text]-curvature tensors for IK-normal complex contact metric manifolds. We have shown that there is no IK-normal complex contact metric manifold with constant sectional curvature and an IK-normal complex contact metric manifold is not Ricci semi-symmetric.

scholarly journals On Projective φ-Recurrent Kenmotsu Manifolds

2005 ◽  
Vol 4 (2) ◽  
pp. 15-21
Author(s):  
C. S. Bagewadi ◽  
S. Venkatesha
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds

In this paper we study a projective φ- recurrent Kenmotsu manifold and show that projective φ- recurrent Kenmotsu manifold having a non-zero constant sectional curvature is locally projective φ-symmetric.

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 On the geometry of lightlike submanifolds of indefinite statistical manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050099
Author(s):  
Varun Jain ◽  
Amrinder Pal Singh ◽  
Rakesh Kumar
Keyword(s):  
Sectional Curvature ◽  
Classical Theory ◽  
Ricci Tensor ◽  
Statistical Manifolds ◽  
Lightlike Submanifolds ◽  
Statistical Submanifold ◽  
Lightlike Submanifold

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore, we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

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 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.

Sign in / Sign up

Export Citation Format

Share Document