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Naturally reductive homogeneous $(α,β)$-metric spaces

Mojtaba Parhizkar, Hamid Reza Salimi Moghaddam

Abstract

In the present paper we study naturally reductive homogeneous $(α,β)$-metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous $(α,β)$-metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler space, given in literature, are equivalent. Finally we compute the flag curvature of naturally reductive homogeneous $(α,β)$-metric spaces.

Naturally reductive homogeneous $(α,β)$-metric spaces

Abstract

In the present paper we study naturally reductive homogeneous -metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous -metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler space, given in literature, are equivalent. Finally we compute the flag curvature of naturally reductive homogeneous -metric spaces.

Paper Structure

This paper contains 2 sections, 7 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Naturally reductive homogeneous $(\alpha,\beta)$-metric spaces

Key Result

Theorem 2.4

If a homogeneous Finsler space $(\frac{G}{H}, F)$ is naturally reductive in the sense of definition def-1, then it must be naturally reductive in the sense of definition def-2.

Theorems & Definitions (19)

  • Definition 1.1
  • Definition 1.2
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Theorem 2.4
  • Corollary 2.5
  • Corollary 2.6
  • proof
  • Theorem 2.7
  • ...and 9 more