Turkish Journal of Mathematics
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 $\mathbb{E}/\tilde{G}$.
DOI
10.3906/mat-1908-15
Keywords
Fiber bundles, isometry group, vector bundles, principal bundles
First Page
378
Last Page
388
Recommended Citation
KADIOĞLU, H (2020). Prolongations of isometric actions to vector bundles. Turkish Journal of Mathematics 44 (2): 378-388. https://doi.org/10.3906/mat-1908-15
