A characterization of compact surfaces with constant mean curvature
Author:
Masaaki Umehara
Journal:
Proc. Amer. Math. Soc. 108 (1990), 483-489
MSC:
Primary 53C42; Secondary 53A10
DOI:
https://doi.org/10.1090/S0002-9939-1990-0987616-2
MathSciNet review:
987616
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Surfaces in a 
-space of constant curvature, whose arbitrary sufficiently small open subsets admit a non-trivial isometric deformation preserving the mean curvature function, are called locally 
-deformable. It is well known that surfaces with constant mean curvature which are not totally umbilical are all locally 
-deformable. Conversely, we shall show in this paper that any compact locally 
-deformable surface has constant mean curvature.
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preserving the mean curvature function, Pacific J. Math. 136 (1989), 71-80. 
, Ann. of Math. 92 (1970), 335-374. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C42, 53A10
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-0987616-2
Keywords:
Surfaces with constant mean curvature,
-deformation
Article copyright:
© Copyright 1990
American Mathematical Society
