Transactions of the American Mathematical Society · 1970 · 79 citations · 2 references
Natural SciencesAstronomyRelativityCurved SpacetimeDifferential GeometryHarmonic AnalysisRiemannian GeometrySpacetime GeometryCovariant DerivativesGauss MapHarmonic MapsMean CurvatureSubmanifold Theory
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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Purdue University, La Fayette, Indiana
Scientific American · 1895 · 28 citations