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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… Click to show full 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 isometries on E form an imbedded Lie subgroup Ge 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/Ge. Key words: Fiber bundles, isometry group, vector bundles, principal bundles
Journal Title: Turkish Journal of Mathematics
Year Published: 2020
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