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On asthenoKähler metrics
"... Abstract. A Hermitian metric on a complex manifold of complex dimension n is called asthenoKähler if its fundamental 2form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂closed. We prove that a conformally balanced asthenoKähler metric on a compact manifod of complex dimensi ..."
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Abstract. A Hermitian metric on a complex manifold of complex dimension n is called asthenoKähler if its fundamental 2form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂closed. We prove that a conformally balanced asthenoKähler metric on a compact manifod of complex dimension n ≥ 3, whose Bismut connection has (restricted) holonomy contained in SU(n), is necessarily Kähler. We provide compact examples of locally conformally balanced asthenoKähler manifolds of complex dimension 3 for which the trace of R B ∧R B vanishes, where R B is the curvature of their Bismut connection. We study blowups of asthenoKähler manifolds for which ∂∂F = 0 and ∂∂F 2 = 0 and we apply these results to orbifolds. Finally, we construct a family of asthenoKähler 2step nilmanifolds of complex dimension 4, showing that, in general, for n> 3, there is no relation between the asthenoKähler and strong KT condition. 1.
Blowups and resolutions of strong Kähler with torsion metrics
, 2009
"... On a compact complex manifold we study the behaviour of strong Kähler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the analogous result of Miyaoka extension theorem. Studying the b ..."
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Cited by 8 (6 self)
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On a compact complex manifold we study the behaviour of strong Kähler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the analogous result of Miyaoka extension theorem. Studying the blowup of a strong KT manifold at a point or along a complex submanifold, we prove that a complex orbifold endowed with a strong KT metric admits a strong KT resolution. In this way we obtain new examples of compact simplyconnected strong KT manifolds.
NONKÄHLER SOLVMANIFOLDS WITH GENERALIZED KÄHLER STRUCTURE
, 2008
"... Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are to ..."
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Cited by 4 (2 self)
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Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are tori. 1.
Formality in generalized Kähler geometry
, 2008
"... We prove that no nilpotent Lie algebra admits an invariant generalized Kähler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kähler case, while it is never formal for a generalized complex struct ..."
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We prove that no nilpotent Lie algebra admits an invariant generalized Kähler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kähler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.
AN EXAMPLE OF 6DIMENSIONAL COMPACT GENERALIZED KÄHLER MANIFOLD
, 2007
"... Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial generalized Kähler structure and which does not admit any Kähler metric. 1. ..."
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Abstract. We construct a compact 6dimensional solvmanifold endowed with a nontrivial generalized Kähler structure and which does not admit any Kähler metric. 1.