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TRANSVERSAL INFINITESIMAL AUTOMORPHISMS ON KÄHLER FOLIATIONS

Part of: Global differential geometry

Published online by Cambridge University Press:  02 February 2012

SEOUNG DAL JUNG  and
HUILI LIU
SEOUNG DAL JUNG*
Affiliation:
Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Jeju 690-756, Korea (email: sdjung@jejunu.ac.kr)
HUILI LIU
Affiliation:
Department of Mathematics, Northeastern University, 110004 Shenyang, PR China (email: liuhl@mail.neu.edu.cn)
*
✉For correspondence; e-mail: sdjung@jejunu.ac.kr
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Abstract

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Let ℱ be a Kähler foliation on a compact Riemannian manifold M. If the transversal scalar curvature of ℱ is nonzero constant, then any transversal conformal field is a transversal Killing field; and if the transversal Ricci curvature is nonnegative and positive at some point, then there are no transversally holomorphic fields.

Keywords

transversal Killing fieldtransversal conformal fieldtransversal Jacobi fieldtransversally holomorphic field

MSC classification

Secondary: 53C12: Foliations (differential geometric aspects)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 405 - 415
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

The first author was supported by the National Research Foundation of Korea (NRF) Grant NRF-2011-616-C00040, and the second author was supported by NSFC no. 11111140377.

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