In this paper, we consider half-flat SU(3)-structures and the subclasses of coupled and double structures. In the general case, we show that the intrinsic torsion form w1^- is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneous spaces. We give an example of a left invariant half-flat (non-coupled and non-double) structure inducing an Einstein metric on S^3×S^3 and we show there does not exist any left invariant coupled structure inducing an Ad(S^1)-invariant Einstein metric on it. Finally, we show that there are no coupled structures inducing the Einstein metric on Einstein solvmanifolds and on homogeneous Einstein manifolds of nonpositive sectional curvature.

Half-flat structures inducing Einstein metrics on homogeneous spaces

RAFFERO, ALBERTO
2015

Abstract

In this paper, we consider half-flat SU(3)-structures and the subclasses of coupled and double structures. In the general case, we show that the intrinsic torsion form w1^- is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneous spaces. We give an example of a left invariant half-flat (non-coupled and non-double) structure inducing an Einstein metric on S^3×S^3 and we show there does not exist any left invariant coupled structure inducing an Ad(S^1)-invariant Einstein metric on it. Finally, we show that there are no coupled structures inducing the Einstein metric on Einstein solvmanifolds and on homogeneous Einstein manifolds of nonpositive sectional curvature.
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http://link.springer.com/article/10.1007%2Fs10455-015-9457-1
Half-flat structures; Coupled structures; Einstein metrics; Homogeneous manifolds
Alberto Raffero
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/150154
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