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Transactions of the American Mathematical Society

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The tension field of the Gauss map

Authors: Ernst A. Ruh and Jaak Vilms
Journal: Trans. Amer. Math. Soc. 149 (1970), 569-573
MSC: Primary 53.04
MathSciNet review: 0259768
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Abstract: In this paper it is shown that the tension field of the Gauss map can be identified with the covariant derivative of the mean curvature vector field. Since a map with vanishing tension field is called harmonic the following theorem is obtained as a corollary. The Gauss map of a minimal submanifold is harmonic.

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Keywords: Codazzi equation, energy integral, harmonic map, immersed submanifold, mean curvature vector field, parallel mean curvature, tension field
Article copyright: © Copyright 1970 American Mathematical Society

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