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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Minimal surfaces with constant curvature in $ 4$-dimensional space forms


Author: Katsuei Kenmotsu
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0706526-5
Keywords: Minimal surfaces with constant curvature, minimal immersions of the hyperbolic $ 2$-plane, higher fundamental tensors
Article copyright: © Copyright 1983 American Mathematical Society