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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homogeneous minimal surfaces in Euclidean spheres with flat normal connections


Author: Kichoon Yang
Journal: Proc. Amer. Math. Soc. 94 (1985), 119-122
MSC: Primary 53C42; Secondary 58A17
MathSciNet review: 781068
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Abstract: We classify, up to congruence, homogeneous minimal surfaces in Euclidean spheres with flat normal connections. The parameter varieties in the space of contact invariants of E. Cartan are computed for all codimensions.


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

  • [1] E. Cartan, Théorie des groupe finis et continues et la géométrie différentielle traitées par la méthode du repère mobile, Gauthier-Villars, Paris, 1937.
  • [2] -, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945.
  • [3] Wu-yi Hsiang, Remarks on closed minimal submanifolds in the standard Riemannian 𝑚-sphere, J. Differential Geometry 1 (1967), 257–267. MR 0225244 (37 #838)
  • [4] Gary R. Jensen, Higher order contact of submanifolds of homogeneous spaces, Lecture Notes in Mathematics, Vol. 610, Springer-Verlag, Berlin-New York, 1977. MR 0500648 (58 #18226)
  • [5] K. Yang, Prolongations of exterior differential systems, preprint 1982.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781068-1
PII: S 0002-9939(1985)0781068-1
Article copyright: © Copyright 1985 American Mathematical Society