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Harmonic G-structures

Published online by Cambridge University Press:  01 March 2009

J. C. GONZÁLEZ–DÁVILA  and
F. MARTÍN CABRERA
J. C. GONZÁLEZ–DÁVILA
Affiliation:
Department of Fundamental Mathematics, University of La Laguna, 38200 La Laguna, Tenerife, Spain. e-mail: [email protected], [email protected]
F. MARTÍN CABRERA
Affiliation:
Department of Fundamental Mathematics, University of La Laguna, 38200 La Laguna, Tenerife, Spain. e-mail: [email protected], [email protected]
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Abstract

For closed and connected subgroups G of SO(n), we study the energy functional on the space of G-structures of a (compact) Riemannian manifold (M, 〈⋅, ⋅〉), where G-structures are considered as sections of the quotient bundle (M)/G. We deduce the corresponding first and second variation formulae and the characterising conditions for critical points by means of tools closely related to the study of G-structures. In this direction, we show the rôle in the energy functional played by the intrinsic torsion of the G-structure. Moreover, we analyse the particular case G=U(n) for 2n-dimensional manifolds. This leads to the study of harmonic almost Hermitian manifolds and harmonic maps from M into (M)/U(n).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 435 - 459
Copyright
Copyright © Cambridge Philosophical Society 2008

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