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arXiv · 2206.08207

On Minkowskian Product of Finsler Manifolds

Jiahui Li·Yong He·Chang Tian·Na Zhang
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Abstract

Let (M_1,F_1) and (M_2,F_2) be a pair of Finsler manifolds. The Minkowskian product Finsler manifold (M,F) of (M_1,F_1) and (M_2,F_2) with respect to a product function f is the product manifold M=M_1\times M_2 endowed with the Finsler metric F^2=f(K,H), where K=(F_1)^2,H=(F_2)^2. In this paper, the Cartan connection and Berwald connection of (M,F) are derived in terms of the corresponding objects of (M_1,F_1) and (M_2,F_2). Necessary and sufficient conditions for (M,F) to be Berwald (resp. weakly Berwald, Landsberg, weakly Landsberg) manifold are obtained. Thus an effective method for constructing special Finsler manifolds mentioned above is given.

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Jiahui Li, Yong He, Chang Tian, Na Zhang. 2022-06-16. On Minkowskian Product of Finsler Manifolds. https://arxiv.org/abs/2206.08207

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