English

Harmonic G-structures

Differential Geometry 2009-11-13 v4

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 O(M)/G. Then, we deduce the corresponding first and second variation formulae and the characterising conditions for critical points by means of tools closely related with the study of G-structures. In this direction, we show the role in the energy functional played by the intrinsic torsion of the G-structure. Moreover, we analyse the particular case G=U(n) for even-dimensional manifolds. This leads to the study of harmonic almost Hermitian manifolds and harmonic maps from M into O(M)/U(n).

Keywords

Cite

@article{arxiv.0706.0116,
  title  = {Harmonic G-structures},
  author = {J. C. Gonzalez Davila and F. Martin Cabrera},
  journal= {arXiv preprint arXiv:0706.0116},
  year   = {2009}
}
R2 v1 2026-06-21T08:34:12.927Z