Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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INFINITESIMAL HOLONOMY ISOMETRIES AND THE CONTINUITY OF HOLONOMY DISPLACEMENTS

  • Byun, Taechang (Department of Mathematics and statistics Sejong University)
  • Received : 2020.04.29
  • Accepted : 2020.08.05
  • Published : 2020.08.15
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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.

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Acknowledgement

The author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2018R1D1A1A02047995).

References

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