INFINITESIMAL HOLONOMY ISOMETRIES AND THE CONTINUITY OF HOLONOMY DISPLACEMENTS

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 e K 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.

1. introduction

2. Infinitesimal holonomy isometries

3. The Iwasawa decomposition

4. Example

5. The continuity of holonomy displacements

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