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Proceedings of the American Mathematical Society

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

 
 

 

On surfaces in $ {\bf R}\sp 4$


Author: Walter Seaman
Journal: Proc. Amer. Math. Soc. 94 (1985), 467-470
MSC: Primary 53A07; Secondary 53C40, 58E20
DOI: https://doi.org/10.1090/S0002-9939-1985-0787896-0
MathSciNet review: 787896
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Abstract: We provide answers (Theorem C) to some questions concerning surfaces in $ {{\mathbf{R}}^4}$ and maps into the quadric $ {Q_2}$ raised by D. Hoffman and R. Osserman.


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

  • [1] D. Hoffman and R. Osserman, The Gauss map of surfaces in $ {{\mathbf{R}}^n}$, J. Differential Geom. 18 (1983). MR 730925 (85i:53059)
  • [2] -, The Gauss map of surfaces in $ {{\mathbf{R}}^3}$ and $ {{\mathbf{R}}^4}$ (to appear).
  • [3] K. Kenmotsu, Weierstrass formula for surfaces of prescribed mean curvature, Math. Ann. 245 (1979), 89-99. MR 552581 (81c:53005b)
  • [4] E. Ruh and J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569-573. MR 0259768 (41:4400)
  • [5] B. Lawson, Complete minimal surfaces in $ {S^3}$, Ann. of Math. (2) 92 (1970), 335-374. MR 0270280 (42:5170)

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DOI: https://doi.org/10.1090/S0002-9939-1985-0787896-0
Article copyright: © Copyright 1985 American Mathematical Society

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