Prolongations of isometric actions to vector bundles

Authors : Hülya Kadioğlu

Pages : 378-388

Doi:10.3906/mat-1908-15

View : 12 | Download : 11

Publication Date : 9999-12-31

Article Type : Makaleler

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
Keywords : Fiber bundles, isometry group, vector bundles, principal bundles