2009
DOI: 10.1017/s0305004108001709
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Harmonic G-structures

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-s… Show more

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Cited by 19 publications
(39 citation statements)
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“…Given a closed and connected subgroup G of SO(n), a G-structure on (M, ·, · ) is a reduction G(M ) ⊂ SO(M ) to G. In the present Section we briefly recall some notions relative to G-structures (see [10,27] for more details).…”
Section: Preliminariesmentioning
confidence: 99%
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“…Given a closed and connected subgroup G of SO(n), a G-structure on (M, ·, · ) is a reduction G(M ) ⊂ SO(M ) to G. In the present Section we briefly recall some notions relative to G-structures (see [10,27] for more details).…”
Section: Preliminariesmentioning
confidence: 99%
“…Thus, in [10] is considered the particular situation for G-structures defined on an oriented Riemannian manifold M of dimension n, where G is a closed and connected subgroup of SO(n). Since the existence of a G-structure on M is equivalent to the existence of a global section σ : M → SO(M )/G of the quotient bundle, the energy of a G-structure is defined as the energy of the corresponding map σ.…”
Section: Introductionmentioning
confidence: 99%
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“…An almost Hermitian manifolds (M, g = ·, · , J ) is called nearly Kähler if J satisfies (∇ X J )X = 0, for all vector fields X on M, or equivalently, ξ is totally skew-symmetric. On nearly Kähler manifolds, ∇ U(n) ξ = 0 (see [6,11]) and we have…”
Section: Preliminariesmentioning
confidence: 99%
“…According with [6], the inner product ·, · is then the restriction to m of a bi-invariant product on g. Because g is semisimple, we take ·, · = − 1 2 B |m , where B denotes the Killing form of g.…”
Section: Proof Of Theorem 11mentioning
confidence: 99%