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Metric Structures on Fibered Manifolds Through Partitions of Unity

Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.4, No. 2)

Publication Date:

Authors : ; ;

Page : 266-272

Keywords : Partitions of Unity fiber bundles Riemannian metric;

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Abstract

The notion of partitions of unity is extremely useful as it allows one to extend local constructions on Euclidean patches to global ones. It is widely used in many fields in mathematics. Therefore, prolongation of this useful tool to another manifold may help constructing many geometric structures. In this paper, we construct a partition of unity on a fiber bundle by using a given partition of unity on the base manifold. On the other hand we show that the converse is also possible if it is a vector bundle. As an application, we define a Riemannian metric on the fiber bundle by using induced partition of unity on the fiber bundle.

Last modified: 2016-10-30 05:09:52