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).Comment: 27 pages, minor correction
We consider three-dimensional contact metric manifolds whose unit characteristic vector field is harmonic or minimal. (2000): 53C25.
Mathematics Subject Classification
We treat Killing-transversally symmetric spaces (briefly, KTS-spaces), that is, Riemannian manifolds equipped with a complete unit Killing vector field such that the reflections with respect to the flow lines of that field can be extended to global isometries. Such manifolds are homogeneous spaces equipped with a naturally reductive homogeneous structure and they provide a rich set of examples of reflection spaces. We prove that each simply connected reducible
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