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On the shape operator of surfaces in space forms

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Abstract

Necessary and sufficient conditions are studied for the existence of surfaces in space forms with prescribed shape operator S. We consider three cases: that of the non-existence of a solution, the case of a unique solution and that of more than one solution. Examples are given for local and global S-deformations and S-rigidity.

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Authors and Affiliations

  1. Departement Mathematik, ETH Zürich, Private Address: Wabergstr. 19, CH-8624, Grüt, Switzerland

    Konrad Voss

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  1. Konrad Voss
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Correspondence to Konrad Voss.

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Dedicated to S. S. Chern on the occasion of his 90th birthday

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Voss, K. On the shape operator of surfaces in space forms. Results. Math. 40, 310–320 (2001). https://doi.org/10.1007/BF03322714

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  • DOI: https://doi.org/10.1007/BF03322714

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