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Tight surfaces in three-dimensional compact Euclidean space forms
Author(s):
Marc-Oliver
Otto
Journal:
Trans. Amer. Math. Soc.
355
(2003),
4847-4863.
MSC (2000):
Primary 53C42;
Secondary 57M50
Posted:
July 28, 2003
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Abstract:
In this paper we define and discuss tight surfaces -- smooth or polyhedral -- in three-dimensional compact Euclidean space forms and prove existence and non-existence results. It will be shown that all orientable and most of the non-orientable surfaces can be tightly immersed in any of these space forms.
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Additional Information:
Marc-Oliver
Otto
Affiliation:
Department of Mathematics, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
Email:
Otto@mathematik.uni-stuttgart.de
DOI:
10.1090/S0002-9947-03-03112-X
PII:
S 0002-9947(03)03112-X
Keywords:
Tight immersions,
tight embeddings,
Euclidean space forms,
total absolute curvature
Received by editor(s):
May 28, 2001
Received by editor(s) in revised form:
May 29, 2002
Posted:
July 28, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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