Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Minimal surfaces in $ S^{m}$ with Gauss curvature $ \leq 0$


Author: Bang-yen Chen
Journal: Proc. Amer. Math. Soc. 31 (1972), 235-238
MSC: Primary 53.04
DOI: https://doi.org/10.1090/S0002-9939-1972-0286000-6
MathSciNet review: 0286000
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Closed minimal surfaces in a unit $ m$-sphere $ {S^m}$ with Gauss curvature $ K \leqq 0$ are considered.


References [Enhancements On Off] (What's this?)

  • [1] B.-Y. Chen, Minimal hypersurfaces in an $ m$-sphere, Proc. Amer. Math. Soc. 29 (1971), 375-380. MR 0285999 (44:3216)
  • [2] S. S. Chern, M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Felds, Springer-Verlag, New York, 1970, pp. 59-75. MR 0273546 (42:8424)
  • [3] H. B. Lawson, Jr., Minimal varieties in constant curvature manifolds, Thesis, Stanford University, Stanford, Calif., 1969.
  • [4] -, Complete minimal surfaces in $ {S^3}$, Ann. of Math. (2) 92 (1970), 335-374. MR 0270280 (42:5170)
  • [5] -, The global behavior of minimal surfaces in $ {S^n}$, Ann. of Math. (2) 92 (1970), 224-237. MR 0270279 (42:5169)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53.04

Retrieve articles in all journals with MSC: 53.04


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0286000-6
Keywords: Minimal surfaces, Gauss curvature, flat surfaces, Clifford torus, minimal direction, Lipschitz-Killing curvature
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society