Jump to ContentJump to Main Navigation
Harmonic Morphisms Between Riemannian Manifolds$
Users without a subscription are not able to see the full content.

Paul Baird and John C. Wood

Print publication date: 2003

Print ISBN-13: 9780198503620

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198503620.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 October 2019

Fundamental properties of harmonic morphisms

Fundamental properties of harmonic morphisms

Chapter:
(p.106) 4 Fundamental properties of harmonic morphisms
Source:
Harmonic Morphisms Between Riemannian Manifolds
Author(s):

Paul Baird

John C. Wood

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198503620.003.0004

This chapter characterizes harmonic morphisms between Riemannian manifolds and discusses their basic properties. The first non-constant term of the Taylor series of a harmonic morphism at a point called ‘symbol’ is considered. The tension field of a submersion is related to the mean curvature of the fibres, yielding geometrical criteria for harmonic morphisms that leads to a study of the associated foliations. The chapter concludes with a discussion of the second variation of energy and volume.

Keywords:   symbol, mean curvature, minimal fibres, foliation, second variation

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .