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On skew 2-projectable almost complex structures on T M

Anton Dekrét (1998)

Archivum Mathematicum

We deal with a ( 1 , 1 ) -tensor field α on the tangent bundle T M preserving vertical vectors and such that J α = - α J is a ( 1 , 1 ) -tensor field on M , where J is the canonical almost tangent structure on T M . A connection Γ α on T M is constructed by α . It is shown that if α is a V B -almost complex structure on T M without torsion then Γ α is a unique linear symmetric connection such that α ( Γ α ) = Γ α and Γ α ( J α ) = 0 .

On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2006)

Annales de l’institut Fourier

We give an example of a compact 6-dimensional non-Kähler symplectic manifold ( M , κ ) that satisfies the Hard Lefschetz Condition. Moreover, it is showed that ( M , κ ) is a special generalized Calabi-Yau manifold.

On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.

On the automorphism group of strongly pseudoconvex domains in almost complex manifolds

Jisoo Byun, Hervé Gaussier, Kang-Hyurk Lee (2009)

Annales de l’institut Fourier

In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...

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