Harmonic G-structures
2009 ◽
Vol 146
(2)
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pp. 435-459
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Keyword(s):
AbstractFor 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).
2005 ◽
Vol 16
(09)
◽
pp. 1017-1031
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1994 ◽
Vol 36
(1)
◽
pp. 77-80
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1987 ◽
Vol 30
(2)
◽
pp. 289-293
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1982 ◽
Vol 91
(3)
◽
pp. 441-452
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Keyword(s):
2012 ◽
Vol 10
(02)
◽
pp. 1250080
◽
2013 ◽
Vol 56
(1)
◽
pp. 173-183
◽