Douglas metrics of (\alpha,\beta) type

Changtao Yu

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arXiv · 1609.04109

Douglas metrics of (\alpha,\beta) type

Changtao Yu

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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.

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Changtao Yu. 2016-09-14. Douglas metrics of (\alpha,\beta) type. https://arxiv.org/abs/1609.04109

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