Share This Article:

Minimal Surfaces and Gauss Curvature of Conoid in Fins-ler Spaces with (α, β)-Metrics

Abstract Full-Text HTML Download Download as PDF (Size:235KB) PP. 220-225
DOI: 10.4236/apm.2012.24032    3,713 Downloads   6,807 Views   Citations
Author(s)    Leave a comment


In this paper, minimal submanifolds in Finsler spaces with (α, β)-metrics are studied. Especially, helicoids are also minimal in (α, β)-Minkowski spaces. Then the minimal surfaces of conoid in Finsler spaces with (α, β)-metrics are given. Last, the Gauss curvature of the conoid in the 3-dimension Randers-Minkowski space is studied.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

D. Xie and Q. He, "Minimal Surfaces and Gauss Curvature of Conoid in Fins-ler Spaces with (α, β)-Metrics," Advances in Pure Mathematics, Vol. 2 No. 4, 2012, pp. 220-225. doi: 10.4236/apm.2012.24032.


[1] Z. Shen, “On Finsler Geometry of Submanifolds,” Mathematische Annalen, Vol. 311, No. 3, 1998, pp. 549- 576. doi:10.1007/s002080050200
[2] M. Souza, J. Spruck, K. Tenenblat, “A Bernstein Type theorem on a Randers Space,” Mathematische Annalen, Vol. 329, No. 2, 2004, pp. 291-305. doi:10.1007/s00208-003-0500-3
[3] Q. He and Y. B. Shen, “On the Mean Curvature of Finsler submanifolds,” Chinese Journal of Contemporary Mathematics, Vol. 27C, 2006, pp. 431-442.
[4] Q. He and Y. B. Shen, “On Bernstein Type Theorems in Finsler Spaces with the Volume form Induced from the Projective Sphere Bundle,” Proceedings of the American Mathematical Society, Vol. 134, No. 3, 2006, pp. 871-880. doi:10.1090/S0002-9939-05-08017-2
[5] M. Souza, K. Tenenblat, “Minimal Surfaces of Rotation in a Finsler Space with a Randers Metric,” Mathematische Annalen, Vol. 325, No. 4, 2003, pp. 625-642. doi:10.1007/s00208-002-0392-7
[6] Q. He, W. Yang, “The Volume Forms and Minimal Surfaces of Rotation in Finsler Spaces with (α, β)-Metrics,” International Journal of Mathematics, Vol. 21, No. 11, 2010, pp. 1401-1411. doi:10.1142/S0129167X10006483
[7] N. Cui and Y. B. Shen, “Minimal Rotated Hypersurface in Minkowski (α, β)-Space,” Geometriae Dedicata, Vol. 151, No. 1, 2010, pp. 27-39. doi:10.1007/s10711-010-9517-4
[8] H. Rund, “The Differential Geometry of Finsler Spaces,” Springer-Verlag, Berlin, 1959.
[9] Z. Shen, “Landsberg Curvature, S-curvature and Riemann Curvature,” In: Z. Shen, Ed., A Sampler of Finsler Geometry, MSRI Series, Cambridge University Press, Cambridge, 2004.
[10] Z. Shen, “Differtial Geometry of Spray and Finsler Spaces,” Kluwer Academic Publishers, Berlin, 2001.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.