Prolongations of isometric actions to vector bundles


Kadıoğlu H.

TURKISH JOURNAL OF MATHEMATICS, vol.44, pp.378-388, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1908-15
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.378-388

Abstract

In this paper, we define an isometry on a total space of a vector bundle E by using a given isometry on the base manifold M . For this definition, we assume that the total space of the bundle is equipped with a special metric which has been introduced in one of our previous papers. We prove that the set of these derived isometrics on E form an imbedded Lie subgroup (G) over tilde of the isometry group I(E) . Using this new subgroup, we construct two different principal bundle structures based one on E and the other on the orbit space E/(G) over tilde.