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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
Posted:
July 19, 2005
MathSciNet review:
2180905
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Additional Information
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:
http://dx.doi.org/10.1090/S0002-9939-05-08017-2
PII:
S 0002-9939(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
Posted:
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 after
28 years from publication.
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