2011•Interdisciplinary Information SciencesOpen access

A Stability Property of Mean Curvature Vectors of Codimension-One Foliations

Gen-ichi Oshikiri

Abstract

In this paper, we show a stability property of mean curvature vector fields of codimension-one foliations with respect to small perturbations of the given codimension-one foliation. This is an extended form of D. Sullivan’s result: If a codimension-one foliation is geometrically taut then any foliation sufficiently close to the foliation is also geometrically taut.

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Key concepts: Foliation (geology), Codimension, Mathematics, Curvature, Pure mathematics, Mean curvature, Property (philosophy), Mathematical analysis