publication . Preprint . 2011

Vector Fields on Product Manifolds

Kurz, Stefan;
Open Access English
  • Published: 05 Jun 2011
Abstract
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.
Subjects
free text keywords: Mathematics - Differential Geometry
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[1] Jet Nestruev. Smooth Manifolds and Observables. Springer, New York, 2003.

[2] Alexandre Vinogradov and Alessandro De Paris. Fat Manifolds and Linear Connections. World Scientific, 2009.

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