ON SOME SPACES OF MINIMAL GEODESICS IN RIEMANNIAN SYMMETRIC SPACES
ON SOME SPACES OF MINIMAL GEODESICS IN RIEMANNIAN SYMMETRIC SPACES
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关于黎曼对称空间中极小测地线的一些空间
DOI：
10.1093/qmath/har003
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
P. Quast
中科院分区：
文献类型：
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作者：
A. Mare;P. Quast
设(P，O)是紧型的点不可约对称空间。本文研究了P中从o到(P，o)中心点的极小(即最短)测地线空间。更准确地说，我们首先给出这些测地线的完整描述。然后，我们证明了由这些测地线的中点所描述的轨迹的每个连通分支都是一个外对称空间(对称R-空间)，它完全测地且等距嵌入在P中。
Let (P, o) be a pointed irreducible symmetric space of compact type. In this paper, we study the space of minimal (i.e. shortest) geodesics in P from o to a point in the center of (P, o). More precisely, we first give a complete description of these geodesics. We then show that each connected component of the locus described by the midpoints of these geodesics is an extrinsically symmetric space (symmetric R-space) which is totally geodesically and isometrically embedded in P.