Douglas metrics of (\alpha,\beta) type
Differential Geometry
2016-09-15 v1
Abstract
In this paper, the Douglas curvature of (\alpha,\beta)-metrics, a special class of Finsler metrics defined by a Riemannian metric \alpha and a 1-form \beta, is studied. These metrics with vanishing Douglas curvature in dimension n\geq3 are classified by using a new class of metrical deformations called \beta-deformations. The result shows that conformal 1-forms of Riemannian metrics play a key role, and an effective way to construct such 1-forms is provided also by \beta-deformations.
Cite
@article{arxiv.1609.04109,
title = {Douglas metrics of (\alpha,\beta) type},
author = {Changtao Yu},
journal= {arXiv preprint arXiv:1609.04109},
year = {2016}
}
Comments
11 pages, 1 figure