Open Access
Translator Disclaimer
Spring 2005 Some properties of mean curvature vectors for codimension-one foliations
Gen-ichi Oshikiri
Illinois J. Math. 49(1): 159-166 (Spring 2005). DOI: 10.1215/ijm/1258138312

Abstract

Given a codimension-one foliation $\mathcal F$ of a closed manifold $M$ and a vector field $X$ on $M$, we show that if $X$ is transverse to $\mathcal F$, then there are many functions $f$ on $M$ so that $fX$ is the mean curvature vector of $\mathcal F$ with respect to some Riemannian metric on $M$. Further we give a necessary and sufficient condition for $X$ to become the mean curvature vector of $\mathcal F$ with respect to some Riemannian metric on $M$.

Citation

Download Citation

Gen-ichi Oshikiri. "Some properties of mean curvature vectors for codimension-one foliations." Illinois J. Math. 49 (1) 159 - 166, Spring 2005. https://doi.org/10.1215/ijm/1258138312

Information

Published: Spring 2005
First available in Project Euclid: 13 November 2009

zbMATH: 1137.53322
MathSciNet: MR2165008
Digital Object Identifier: 10.1215/ijm/1258138312

Subjects:
Primary: 53C12

Rights: Copyright © 2005 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.49 • No. 1 • Spring 2005
Back to Top