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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 $\mathbb{E}/\tilde{G}$.

First Page

378

Last Page

388

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Mathematics Commons

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