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

页码：954 / 969

页数：16

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