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Transformation Groups

, Volume 22, Issue 4, pp 1143–1183 | Cite as

NORMAL HOMOGENEOUS FINSLER SPACES

  • MING XU
  • SHAOQIANG DENGEmail author
Article

Abstract

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space using the method of isometric submersion of Finsler metrics. Then we study the geometric properties. In particular, we establish a technique to reduce the classification of normal homogeneous Finsler spaces of positive flag curvature to an algebraic problem. The main result of this paper is a classification of positively curved normal homogeneous Finsler spaces. It turns out that a coset space G/H admits a positively curved normal homogeneous Finsler metric if and only if it admits a positively curved normal homogeneous Riemannian metric. We will also give a complete description of the coset spaces admitting non-Riemannian positively curved normal homogeneous Finsler spaces.

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.College of MathematicsTianjin Normal UniversityTianjinChina
  2. 2.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina

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