Structure of a leaf of some codimension one Riemannian foliation
type: Item
instance of: scholarly article
title: Structure of a leaf of some codimension one Riemannian foliation
zbMATH Open document ID: 0652.53024
author: Krystyna Bugajska
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74788
review text: Let \(M\) be a smooth connected open orientable finite-dimensional manifold endowed with a smooth codimension one Riemannian foliation \(F\). The purpose of this paper is to study the geometric structure of a leaf \(L\) of \(F\) when \(F\) is a totally geodesic foliation. Let \(f\) be a map given by \(f(x) = (x,n(x),m \rho)\), \(x \in L\), where \(x \to n(x)\) is a normal field of unit vectors, \(m \in Z^+\) and \(\rho\) is a positive constant depending on \(F\). The author shows that: 1) There exists a vector \(V\) on \(L\) such that \(f(x) = \exp e_L(x)V(x)\), where the range \(e_L(x)\) is the greatest lower bound of the lengths of minimizing geodesics joining two variable points in the \(L\)-submanifold; 2) The leaf \(L\) is of fibred type over a complete Riemannian manifold \(N\) with boundary.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4063972
zbMATH Keywords: open leaf
zbMATH Keywords: non-positive curvature
zbMATH Keywords: range of a point
zbMATH Keywords: codimension one Riemannian foliation
zbMATH Keywords: totally geodesic foliation
Wikidata QID: Q115159073
MaRDI profile type: Publication
OpenAlex ID: W2061373762
cites work: COMPLEMENTARY DISTRIBUTIONS WHICH PRESERVE THE LEAF GEOMETRY AND APPLICATIONS TO TOTALLY GEODESIC FOLIATIONS
cites work: On complete open manifolds of positive curvature
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cites work: Q5731354
cites work: Foliated manifolds with bundle-like metrics
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cites work: Remarks on the group of isometries of a Riemannian manifold
DOI: 10.5802/AIF.1128
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4063972