Journal ArticleDOI
Neutral Calabi-Yau Structures on Kodaira Manifolds
TLDR
In this article, neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds are constructed, and the structures are symmetric with respect to the central tori.Abstract:
We construct neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds. Our structures are symmetric with respect to the central tori.read more
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Families of strong KT structures in six dimensions
TL;DR: In this article, the authors classify Ricci-flat structures on 6-dimensional nilmanifolds for which the fundamental 2-form is closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such structures is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limacon-shaped curve in the complex plane.
Journal ArticleDOI
ParaHermitian and paraquaternionic manifolds
Stefan Ivanov,Simeon Zamkovoy +1 more
TL;DR: In this paper, it is proved that the Nijenhuis tensor of a Nearly paraKahler manifold is parallel with respect to the canonical connection, and an anti-self-dual neutral metric which is not locally conformally hyper-para-kahler is constructed.
Posted Content
Families of strong KT structures in six dimensions
TL;DR: In this article, the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group and explicit solutions are obtained from a limacon-shaped curve in the complex plane.
Journal ArticleDOI
Homogeneous para-Kähler Einstein manifolds
TL;DR: In this article, it was shown that any invariant para-complex structure on a semisimple Lie group defines a unique para-Kahler Einstein structure with given nonzero scalar curvature.
Journal ArticleDOI
Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures
Maciej Dunajski,S. West +1 more
TL;DR: In this article, the twistor space of a real analytic neutral signature anti-self-dual conformal structure (M, [g]) with a null conformal Killing vector is constructed.
References
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Book
Compact Complex Surfaces
TL;DR: In this article, the authors describe the topology and algebraic properties of complex surfaces, including the following properties: 1. The Projective Plane, 2. The Jacobian Fibration, 3. Hodge Theory on Surfaces, 4. Inequahties for Hodge Numbers, 5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch Theorem.
Journal ArticleDOI
Real Homotopy Theory of Kähler Manifolds.
TL;DR: In this paper, the De Rham Complex of a Compact K~ihler Manifold has been shown to be a homotopy theory of differential algebras.
Journal ArticleDOI
Some simple examples of symplectic manifolds
TL;DR: In this article, Liberman et al. gave a construction of closed symplectic manifolds with no Kaehler structure, and showed that such manifolds do not have even odd Betti numbers.
Journal ArticleDOI
Complex structures on nilpotent Lie algebras
TL;DR: In this paper, the authors classify real six-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.