Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kurz, Stefan
Institution: Tampere University of Technology
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1634284113