Minimal immersed manifold: Difference between revisions
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{{Riemannian metric property}} | {{Riemannian metric property}} | ||
{{zeroproperty|[[Mean curvature]]}} | |||
==Definition== | ==Definition== | ||
Latest revision as of 19:49, 18 May 2008
This article defines a property that makes sense for a Riemannian metric over a differential manifold
This is the property of the following curvature being everywhere zero: Mean curvature
Definition
Symbol-free definition
A Riemannian manifold (viz a differential manifold equipped with a Riemannian metric) is termed a minimal manifold if the mean curvature of the manifold is zero at all points. This is a generalization to the manifold setting of the notion of a minimal surface.