A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow

We prove that a Riemannian foliation with the flat normal connection on a Riemannian manifold is harmonic if and only if the geodesic flow on the normal bundle preserves the Riemannian volume form of the canonical metric defined by the adapted connection.

Bibliographic Details
Main Author:	Hobum Kim
Format:	Article
Language:	English
Published:	Hindawi Limited 2002-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/S0161171202007822

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spelling	doaj-fa41da532da344b2a8808777cdd0f8ba2020-11-24T23:35:34ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01291057357710.1155/S0161171202007822A characterization of harmonic foliations by the volume preserving property of the normal geodesic flowHobum Kim0Department of Mathematics, Yonsei University, Seoul 120-749, KoreaWe prove that a Riemannian foliation with the flat normal connection on a Riemannian manifold is harmonic if and only if the geodesic flow on the normal bundle preserves the Riemannian volume form of the canonical metric defined by the adapted connection.http://dx.doi.org/10.1155/S0161171202007822
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hobum Kim
spellingShingle	Hobum Kim A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow International Journal of Mathematics and Mathematical Sciences
author_facet	Hobum Kim
author_sort	Hobum Kim
title	A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
title_short	A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
title_full	A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
title_fullStr	A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
title_full_unstemmed	A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
title_sort	characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2002-01-01
description	We prove that a Riemannian foliation with the flat normal connection on a Riemannian manifold is harmonic if and only if the geodesic flow on the normal bundle preserves the Riemannian volume form of the canonical metric defined by the adapted connection.
url	http://dx.doi.org/10.1155/S0161171202007822
work_keys_str_mv	AT hobumkim acharacterizationofharmonicfoliationsbythevolumepreservingpropertyofthenormalgeodesicflow AT hobumkim characterizationofharmonicfoliationsbythevolumepreservingpropertyofthenormalgeodesicflow
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A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow

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