The exponential map on the free loop space is Fredholm

被引：11
作者：
Misiolek, G [1 ]
机构：
[1] UNIV NOTRE DAME,DEPT MATH,NOTRE DAME,IN 46556
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 1997年 / 7卷 / 05期
关键词：
Riemannian Manifold; Loop Space; Conjugate Point; Index Zero; Free Loop Space;
D O I：
10.1007/s000390050032
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the exponential map on Hilbert riemannian manifolds and show that on the free loop space Omega M-n = H-1(S-1, M-n) it is a nonlinear Fredholm map of index zero. Among corollaries we obtain that only one type of conjugate points exists in Omega M-n. This answers a question of W. Klingenberg.
引用
收藏
页码：954 / 969
页数：16
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