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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1970-0259768-5
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0259768-5
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