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)

 
 

 

A local classification of $ 2$-type surfaces in $ S\sp 3$


Authors: Th. Hasanis and Th. Vlachos
Journal: Proc. Amer. Math. Soc. 112 (1991), 533-538
MSC: Primary 53C40; Secondary 53A05
DOI: https://doi.org/10.1090/S0002-9939-1991-1059626-1
MathSciNet review: 1059626
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The only spherical surfaces in $ {E^4}$ that are either of $ 1$-type or of $ 2$-type are portions of ordinary spheres, minimal surfaces in $ {S^3}$, and Riemannian products of two plane circles of different radii.


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

  • [1] M. Barros and O. Garay, $ 2$-type surfaces in $ {S^3}$, Geometriae Dedicata 24 (1987), 329-336. MR 914828 (88m:53096)
  • [2] B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore and New Jersey, 1984. MR 749575 (86b:53053)
  • [3] -, $ 2$-type submanifolds and their applications, Chinese J. Math. 14 (1986), 1-14. MR 861185 (87m:53069)
  • [4] B.-Y. Chen and G. D. Ludden, Surfaces with mean curvature vector parallel in the normal bundle, Nagoya Math. J. 47 (1972), 161-167. MR 0331231 (48:9565)
  • [5] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. MR 0198393 (33:6551)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C40, 53A05

Retrieve articles in all journals with MSC: 53C40, 53A05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1059626-1
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society