scholarly journals On Ricci curvature of submanifolds in statistical manifolds of constant (quasi-constant) curvature

2020 ◽  
Vol 5 (4) ◽  
pp. 3495-3509
Author(s):  
Aliya Naaz Siddiqui ◽  
◽  
Mohammad Hasan Shahid ◽  
Jae Won Lee ◽  
Keyword(s):  
Ricci Curvature ◽  
Constant Curvature ◽  
Statistical Manifolds

Inequalities for submanifolds in statistical manifolds of quasi-constant curvature

2018 ◽  
Vol 121 (3) ◽  
pp. 197-215 ◽  
Author(s):  
Hülya Aytimur ◽  
Cihan Özgür
Keyword(s):  
Constant Curvature ◽  
Statistical Manifolds

scholarly journals DEFORMATIONS OF THE VERONESE EMBEDDING AND FINSLER -SPHERES OF CONSTANT CURVATURE

2021 ◽  
pp. 1-32
Author(s):  
Christian Lange ◽  
Thomas Mettler
Keyword(s):  
Ricci Curvature ◽  
Constant Curvature ◽  
Projective Spaces ◽  
Positive Definite ◽  
The Other ◽  
Duality Result ◽  
Veronese Embedding ◽  
Other Hand ◽  
The One ◽  
Weyl Connections

Abstract We establish a one-to-one correspondence between, on the one hand, Finsler structures on the $2$ -sphere with constant curvature $1$ and all geodesics closed, and on the other hand, Weyl connections on certain spindle orbifolds whose symmetric Ricci curvature is positive definite and whose geodesics are all closed. As an application of our duality result, we show that suitable holomorphic deformations of the Veronese embedding $\mathbb {CP}(a_1,a_2)\rightarrow \mathbb {CP}(a_1,(a_1+a_2)/2,a_2)$ of weighted projective spaces provide examples of Finsler $2$ -spheres of constant curvature whose geodesics are all closed.

scholarly journals Some inequalities on submanifolds in statistical manifolds of constant curvature

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 465-477 ◽  
Author(s):  
Muhittin Aydin ◽  
Adela Mihai ◽  
Ion Mihai
Keyword(s):  
Constant Curvature ◽  
Statistical Manifolds

In this paper, we study the behaviour of submanifolds in statistical manifolds of constant curvature. We investigate curvature properties of such submanifolds. Some inequalities for submanifolds with any codimension and hypersurfaces of statistical manifolds of constant curvature are also established.

scholarly journals Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 690 ◽  
Author(s):  
Ali Alkhaldi ◽  
Mohd. Aquib ◽  
Aliya Siddiqui ◽  
Mohammad Shahid
Keyword(s):  
Constant Curvature ◽  
Necessary And Sufficient Condition ◽  
Einstein Field Equations ◽  
Statistical Manifold ◽  
Field Equations ◽  
Space Forms ◽  
Equality Case ◽  
Statistical Manifolds ◽  
Necessary And Sufficient ◽  
Statistical Space

In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Sign in / Sign up

Export Citation Format

Share Document