Tight surfaces in three-dimensional compact Euclidean space forms

Author:
Marc-Oliver Otto

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4847-4863

MSC (2000):
Primary 53C42; Secondary 57M50

DOI:
https://doi.org/10.1090/S0002-9947-03-03112-X

Published electronically:
July 28, 2003

MathSciNet review:
1997587

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-03-03112-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

Published electronically:
July 28, 2003

Article copyright:
© Copyright 2003
American Mathematical Society