Realizability of the $H_k$-distance functions by homology classes of path spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 18-24
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In the previous papers we constructed and studied mappings $d_k\colon M\times M\to\mathbb R$; we called them the $H_k$-distance functions. The main result of this paper is a theorem about the realizability of generalized distances $d_k(v,w)$, $v,w\in M$, considered as critical values of the length functional $\mathcal L\colon\Omega(M,v,w)\to\mathbb R$ generated by some nontrivial homology classes of the space $\Omega(M,v,w)$ of paths between points $v$ and $w$.
Keywords:
Riemannian manifold, path space, distance functions, multivalued functional, extremal.
@article{IVM_2010_5_a2,
author = {Yu. V. Ershov and E. I. Yakovlev},
title = {Realizability of the $H_k$-distance functions by homology classes of path spaces},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {18--24},
publisher = {mathdoc},
number = {5},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2010_5_a2/}
}
TY - JOUR AU - Yu. V. Ershov AU - E. I. Yakovlev TI - Realizability of the $H_k$-distance functions by homology classes of path spaces JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2010 SP - 18 EP - 24 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2010_5_a2/ LA - ru ID - IVM_2010_5_a2 ER -
Yu. V. Ershov; E. I. Yakovlev. Realizability of the $H_k$-distance functions by homology classes of path spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 18-24. http://geodesic.mathdoc.fr/item/IVM_2010_5_a2/