Linear transports along paths in vector bundles. IV. Consistency with bundle metrics

2005/05/01 by Bozhidar Z. Iliev
Mathematics · Physics and Astronomy · #math.DG #math-ph #math.MP #msc:53C99 #msc:53B99 #msc:57R35

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published as Communication JINR, E5-94-17, Dubna, 1994 · 20 LaTeX pages. For related papers, visit the "publication" pages at http://theo.inrne.bas.bg/~bozho/

arxiv created 2005/05/01 · arxiv updated 2009/12/01

Abstract

The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are explicitly obtained. The special case of linear transports, generated by derivations of tensor algebras, of vectors is considered. Analogous problems are investigated in complex vector bundles endowed with Hermitian metrics.

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