期刊
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
卷 56, 期 -, 页码 308-324出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2017.10.002
关键词
Spray; Finsler metrizability; Berwald frame; Frobenius integrability
资金
- Erasmus+ Mobility Project for Higher Education Students and Staff with Partner Countries
For a 2-dimensional non-flat spray we associate a Berwald frame and a 3-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of the given spray. In the integrable case, the sought after Finsler function is provided by a closed, homogeneous 1-form from the annihilator of the Berwald distribution. We discuss both the degenerate and non-degenerate cases using the fact that the regularity of the Finsler function is encoded into a regularity condition of a 2-form, canonically associated to the given spray. The integrability of the Berwald distribution and the regularity of the 2-form have simple and useful expressions in terms of the Berwald frame. (C) 2017 Elsevier B.V. All rights reserved.
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