Minimal surfaces with constant curvature in $4$-dimensional space forms
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- by Katsuei Kenmotsu
- Proc. Amer. Math. Soc. 89 (1983), 133-138
- DOI: https://doi.org/10.1090/S0002-9939-1983-0706526-5
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Abstract:
We classify minimal surfaces with constant Gaussian curvature in a $4$-dimensional space form without any global assumption. As a corollary of the main theorem, we show there is no isometric minimal immersion of a surface with constant negative Gaussian curvature into the unit $4$-sphere even locally. This gives a partial answer to a problem proposed by S. T. Yau.References
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Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 133-138
- MSC: Primary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1983-0706526-5
- MathSciNet review: 706526