Minkowski空间的等价性定理及在Finsler几何的应用

李明

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 177-190.

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数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 177-190. DOI: 10.12386/A2019sxxb0015
论文

Minkowski空间的等价性定理及在Finsler几何的应用

    李明
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On Equivalence Theorems of Minkowski Spaces and Applications in Finsler Geometry

    Ming LI
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文章历史 +

摘要

首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的 Landsberg 空间为 Berwald 空间,这些条件可以是具有闭的 Cartan 型形式,S曲率为零或平均 Berwald曲率为零.

Abstract

We first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As applications in Finsler geometry, we prove that a Finsler manifold is a Berwald space if it is a Landsberg space and satisfies one of the following conditions: closed Cartan-type form, vanishing S curvature or vanishing mean Berwald curvature.

关键词

Minkowski空间 / 卵形超曲面 / Cartan型形式 / 平行移动 / Berwald空间

Key words

Minkowski space / hyperovaloid / Cartan-type form / parallel transport / Berwald space

引用本文

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李明. Minkowski空间的等价性定理及在Finsler几何的应用. 数学学报, 2019, 62(2): 177-190 https://doi.org/10.12386/A2019sxxb0015
Ming LI. On Equivalence Theorems of Minkowski Spaces and Applications in Finsler Geometry. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 177-190 https://doi.org/10.12386/A2019sxxb0015

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基金

国家自然科学基金资助项目(11501067,11571184);the Marie Cuire IRSE Sproject(PIRSES-GA-2012-317721-LIE-DIFF-GEOM)

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