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The graph of a foliation

Name: The graph of a foliation
Creator: H. E. Winkelnkemper
Keywords: second fundamental form, Foliations (differential geometric aspects), sectional curvature, Cartan-Hadamard theorem, 0103 physical sciences, Foliations in differential topology; geometric theory, holonomy, 0101 mathematics, Riemannian foliation, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1983Publisher:Springer Science and Business Media LLCJournal:Annals of Global Analysis and Geometry, volume 1, pages 51-75 (issn: 0617-8043, eissn: 1572-9060,

Authors: H. E. Winkelnkemper;

doi: 10.1007/bf02329732

The graph of a foliation

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- Subjects
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Abstract

Let M be a riemannian manifold with a riemannian foliation F. Among other things we construct a special metric on the graph of the foliation,\(\mathfrak{G}(F)\), (which is complete, when M is complete), and use the relations of Gray [1] and O'Neill [7] and the elementary structural properties of\(\mathfrak{G}(F)\), to find a necessary and sufficient condition that\(\mathfrak{G}(F)\) also have non-positive sectional curvature, when M does.

Related Organizations

University of Maryland, College Park
United States
University of Maryland, Baltimore
United States

Keywords

second fundamental form, Foliations (differential geometric aspects), sectional curvature, Cartan-Hadamard theorem, Foliations in differential topology; geometric theory, holonomy, Riemannian foliation

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	94
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 1%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average