[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2020.33.3.365

INFINITESIMAL HOLONOMY ISOMETRIES AND THE CONTINUITY OF HOLONOMY DISPLACEMENTS

Byun, Taechang (Department of Mathematics and statistics Sejong University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.33, no.3, 2020 , pp. 365-374 More about this Journal

Abstract

Given a noncompact semisimple Lie group G and its maximal compact Lie subgroup K such that the right multiplication of each element in K gives an isometry on G, consider a principal bundle G → G/K, which is a Riemannian submersion. We study the infinitesimal holonomy isometries. Given a closed curve at eK in the base space G/K, consider the holonomy displacement of e by the horizontal lifting of the curve. We prove that the correspondence is continuous.

Keywords

Holonomy displacement; Riemannian submersion; Principal bundle; Iwasawa decomposition;

Citations & Related Records

Reference

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