Turkish Journal of Mathematics
DOI
10.3906/mat-1908-15
Abstract
In this paper, we define an isometry on a total space of a vector bundle $\mathbb{E}$ by using a given isometry on the base manifold $\mathbb{M}$. 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 isometries on $\mathbb{E}$ form an imbedded Lie subgroup $\tilde{G}$ of the isometry group $I(E)$. Using this new subgroup, we construct two different principal bundle structures based one on $\mathbb{E}$ and the other on the orbit space $\mathbb{E}/\tilde{G}$.
Keywords
Fiber bundles, isometry group, vector bundles, principal bundles
First Page
378
Last Page
388
Recommended Citation
KADIOĞLU, HÜLYA
(2020)
"Prolongations of isometric actions to vector bundles,"
Turkish Journal of Mathematics: Vol. 44:
No.
2, Article 3.
https://doi.org/10.3906/mat-1908-15
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss2/3
