Tight surfaces in three-dimensional compact Euclidean space forms

Otto, Marc-Oliver

doi:10.1090/S0002-9947-03-03112-X

Tight surfaces in three-dimensional compact Euclidean space forms
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by Marc-Oliver Otto PDF

Trans. Amer. Math. Soc. 355 (2003), 4847-4863 Request permission

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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