Displaying similar documents to “Vector bundles as an instrument of the metric and conformal differential geometry (Preliminary communication)”

Subtleties concerning conformal tractor bundles

C. Graham, Travis Willse (2012)

Open Mathematics

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The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor...

On the geometry of tangent bundles with a class of metrics

Esmaeil Peyghan, Abbas Heydari, Leila Nourmohammadi Far (2012)

Annales Polonici Mathematici

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We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.