## 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.## References

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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
- 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
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**134**(2006), 871-880 - MSC (2000): Primary 53C60; Secondary 53B40
- DOI: https://doi.org/10.1090/S0002-9939-05-08017-2
- MathSciNet review: 2180905