Vector Fields on Product Manifolds

Details Vector Fields on Product Manifolds Vector Fields on Product Manifolds

2011-06-05

arxiv.org/abs/1106.0926v1

Mathematics

Differential Geometry

Scientific paper

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.

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