Riemannian M-spaces with homogeneous geodesics
Riemannian M-spaces with homogeneous geodesics
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DOI：
10.1007/s10455-018-9603-7
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发表时间：
2016-10
影响因子：
0.7
通讯作者：
A. Arvanitoyeorgos;Yu Wang;Guosong Zhao
中科院分区：
文献类型：
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作者：
A. Arvanitoyeorgos;Yu Wang;Guosong Zhao
本文研究了一类称为M-空间的齐性空间中的齐性测地线。设G/K是一个广义旗流形，其中S是紧致单李群中的环面，G_d是K的半单部分。则伴随M-空间是齐性空间。这些空间是由H. C. 1954年的王。我们证明了对于各种M-空间类，唯一的g.o.公制是标准公制。对于其它M-空间类，我们给出了G-不变度量是G. o的必要条件或充要条件。公制分析是基于旗流形G/K[as-模]的各向同性表示的性质。
We investigate homogeneous geodesics in a class of homogeneous spaces calledM-spaces, which are defined as follows. LetG/Kbe a generalized flag manifold with, whereSis a torus in a compact simple Lie groupGandis the semisimple part ofK. Then, theassociatedM-spaceis the homogeneous space. These spaces were introduced and studied by H. C. Wang in 1954. We prove that for various classes ofM-spaces the only g.o. metric is the standard metric. For other classes ofM-spaces we give either necessary, or necessary and sufficient conditions, so that aG-invariant metric onis a g.o. metric. The analysis is based on properties of the isotropy representationof the flag manifoldG/K[as-modules].