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Publishing Language: Chinese | Open Access

Classification of positively curved homogeneous Finsler spaces: a new approach in the even dimensional case

Xiyun XU, Ming XU( )
School of Mathematical Sciences, Capital Normal University, Beijing 100048
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Abstract

In this paper, we briefly survey the classification of positively curved homogeneous Finsler manifolds. We propose a new method in the even dimensional case, which proves that an even dimensional smooth coset space admits positively curved homogeneous Finsler metrics if and only if it admits positively curved homogeneous Riemannian metrics.

Keywords

flag curvaturehomogeneous Finsler spaceinvariant Finsler metricpositively curved Finsler manifold

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Journal of Capital Normal University (Natural Science Edition)
Volume 45 Issue 1,
February 2024
Pages 124-130
DOI: 10.19789/j.1004-9398.2024.01.012

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XU X, XU M. Classification of positively curved homogeneous Finsler spaces: a new approach in the even dimensional case. Journal of Capital Normal University (Natural Science Edition), 2024, 45(1): 124-130. https://doi.org/10.19789/j.1004-9398.2024.01.012

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Received: 15 October 2023
Published: 01 February 2024
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2025.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).