Hülya Kadıoğlu, Robert J. Fisher
Abstract
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In this paper, we prove that total space of every vector bundle with the base manifold on which the canonical isometric action acts freely, also carries a principal bundle structure. We also obtain another principal bundle based on the total space of given vector bundle.
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In this paper, we prove that total space of every vector bundle with the base manifold on which the canonical isometric action acts freely, also carries a principal bundle structure. We also obtain another principal bundle based on the total space of given vector bundle.
Key concepts: Principal bundle, Vector bundle, Frame bundle, Vector-valued differential form, Bundle, Isometry (Riemannian geometry), Mathematics, Tautological line bundle