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Minimal Surfaces with Constant Curvature in 4-Dimensional Space Forms

Katsuei Kenmotsu
Proceedings of the American Mathematical Society
Vol. 89, No. 1 (Sep., 1983), pp. 133-138
DOI: 10.2307/2045079
Stable URL: http://www.jstor.org/stable/2045079
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Minimal Surfaces with Constant Curvature in 4-Dimensional Space Forms
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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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