Minimal surfaces with constant curvature in 4-dimensional space forms

Kenmotsu, Katsuei

doi:10.1090/S0002-9939-1983-0706526-5

Minimal surfaces with constant curvature in $4$-dimensional space forms
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Proc. Amer. Math. Soc. 89 (1983), 133-138 Request permission

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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