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

Authors:
Qun He and Yi-Bing Shen

Journal:
Proc. Amer. Math. Soc. **134** (2006), 871-880

MSC (2000):
Primary 53C60; Secondary 53B40

Published electronically:
July 19, 2005

MathSciNet review:
2180905

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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 in a Randers space is just that for the Riemannian metric , and therefore the Bernstein type theorem in the special Randers space of dimension is true. Moreover, a Bernstein type theorem in the -dimensional Minkowski space is established by considering the volume form induced from the projective sphere bundle.

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Additional Information

**Qun He**

Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai 200092, People’s Republic of China

Email:
hequn@mail.tongji.edu.cn

**Yi-Bing Shen**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310028, People’s Republic of China

Email:
yibingshen@zju.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-05-08017-2

Keywords:
Finsler volume form,
minimal surface,
Randers space,
Minkowski space

Received by editor(s):
June 4, 2004

Received by editor(s) in revised form:
October 13, 2004

Published electronically:
July 19, 2005

Additional Notes:
The first author was supported in part by NNSFC (no.10471105).

The second author was supported in part by NNSFC (no.10271106).

Communicated by:
Richard A. Wentworth

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.