Umbilic foliations and curvature
type: Item
instance of: scholarly article
title: Umbilic foliations and curvature
zbMATH Open document ID: 0880.53025
author: Gerard Walschap
published in: Illinois Journal of Mathematics
publication date: 1998-02-08T00:00:00Z
review text: The author shows that there are no \(k\)-dimensional umbilic foliations of an \(n\)-dimensional manifold of positive sectional curvature with \(k> {n-1 \over 2}\). In the paper, there are studied umbilic foliations of codimension one on manifolds of nonpositive curvature. The author also proves that an umbilic \(k\)-dimensional foliation \({\mathcal F} (k>1)\) of the complete simply connected space \(M\) of constant curvature \(c\) is flat if \(c\leq 0\), and homogeneous if \(c \geq 0\).
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1029005
zbMATH Keywords: space form
zbMATH Keywords: umbilic foliation
zbMATH Keywords: sectional curvature
reviewed by: Andrzej Piatkowski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1029005