A variational problem for submanifolds of Euclidean space
Author: Joseph A. Erbacher
Journal: Proc. Amer. Math. Soc. 36 (1972), 467-470
MSC: Primary 53C30; Secondary 53C70
MathSciNet review: 0309020
Abstract: Let be a compact differentiable manifold and Euclidean space. A necessary and sufficient condition is given for an immersion to be a stationary immersion for dv subject to the side condition dv= a fixed constant, where is the center of mass. In particular, minimal submanifolds of spheres satisfy this condition.
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Keywords: Compact differentiable manifold, Riemannian, Euclidean space, center of mass, stationary immersion, mean curvature normal, minimal submanifold
Article copyright: © Copyright 1972 American Mathematical Society