On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle

He, Qun; Shen, Yi-Bing

doi:10.1090/S0002-9939-05-08017-2

On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle
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by Qun He and Yi-Bing Shen PDF

Proc. Amer. Math. Soc. 134 (2006), 871-880 Request permission

Abstract:

By using the volume form induced from the projective sphere bundle of the Finsler manifold, we study the Finsler minimal submanifolds. It is proved that such a volume form for the Randers metric $F=\alpha +\beta$ in a Randers space is just that for the Riemannian metric $\alpha$, and therefore the Bernstein type theorem in the special Randers space of dimension $\leq 8$ is true. Moreover, a Bernstein type theorem in the $3$-dimensional Minkowski space is established by considering the volume form induced from the projective sphere bundle.

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