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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
Published electronically: July 28, 2003
MathSciNet review: 1997587
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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: 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