Prolongations of isometric actions to vector bundles

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Kadıoğlu H.

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

  • Publication Type: Article / Article
  • Volume: 44
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1908-15
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.378-388
  • Yıldız Technical University Affiliated: Yes


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.