On transversal infinitesimal automorphisms for harmonic foliations

Philippe Tondeur; Gabor Toth

doi:10.1007/BF00150938

On transversal infinitesimal automorphisms for harmonic foliations

Philippe Tondeur, Gabor Toth

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we consider a harmonic Riemannian foliation ℱ, and study the transversal infinitesimal automorphisms of ℱ with certain additional properties like being transversal conformal or Killing (= metric). Such automorphisms (modulo Killing automorphisms) are related to the stability of ℱ. A special study is made for the case of a foliation with constant transversal scalar curvature, and more particularly with transversal Ricci curvature proportional to the transversal metric (Einstein foliation).

Original language	English (US)
Pages (from-to)	229-236
Number of pages	8
Journal	Geometriae Dedicata
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/BF00150938
State	Published - Oct 1987

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/BF00150938

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abstract = "In this paper we consider a harmonic Riemannian foliation ℱ, and study the transversal infinitesimal automorphisms of ℱ with certain additional properties like being transversal conformal or Killing (= metric). Such automorphisms (modulo Killing automorphisms) are related to the stability of ℱ. A special study is made for the case of a foliation with constant transversal scalar curvature, and more particularly with transversal Ricci curvature proportional to the transversal metric (Einstein foliation).",

author = "Philippe Tondeur and Gabor Toth",

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AB - In this paper we consider a harmonic Riemannian foliation ℱ, and study the transversal infinitesimal automorphisms of ℱ with certain additional properties like being transversal conformal or Killing (= metric). Such automorphisms (modulo Killing automorphisms) are related to the stability of ℱ. A special study is made for the case of a foliation with constant transversal scalar curvature, and more particularly with transversal Ricci curvature proportional to the transversal metric (Einstein foliation).

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On transversal infinitesimal automorphisms for harmonic foliations

Abstract

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