Realizability of the H-k-Distance Functions by Homology Classes of Path Spaces

被引：0

作者：

Ershov, Yu. V. ^{[1
]}

Yakovlev, E. I. ^{[1
]}

机构：

[1] Nizhnii Novgorod State Univ, Pr Gagarina 23, Nizhnii Novgorod 603950, Russia

来源：

RUSSIAN MATHEMATICS | 2010年 / 54卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

Riemannian manifold; path space; distance functions; multivalued functional; extremal;

D O I：

10.3103/S1066369X10050038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In previous papers, we have constructed and studied mappings d(k) : M x M -> R called the Hk- distance functions. The main result of this paper is a theorem on realizability of the generalized distances d(k)( v, w), v, w is an element of M, by critical values of the length functional L : Omega( M, v, w). R generated by nontrivial homology classes of the space Omega( M, v, w) of paths joining the points v and w.

引用

页码：15 / 20

页数：6