Tight surfaces in three-dimensional compact Euclidean space forms
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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.References
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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
- Received by editor(s): May 28, 2001
- Received by editor(s) in revised form: May 29, 2002
- Published electronically: July 28, 2003
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1997587