Displaying similar documents to “Paracomplex projective models and harmonic maps into them.”

Strongly not relatives Kähler manifolds

Michela Zedda (2017)

Complex Manifolds

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In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that...

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Le Mau Hai, Nguyen Van Khue, Pham Hoang Hiep (2007)

Annales Polonici Mathematici

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We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.

Some properties of para-Kähler-Walker metrics

Mustafa Özkan, Murat İşcan (2014)

Annales Polonici Mathematici

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A Walker 4-manifold is a pseudo-Riemannian manifold (M₄,g) of neutral signature, which admits a field of parallel null 2-planes. We study almost paracomplex structures on 4-dimensional para-Kähler-Walker manifolds. In particular, we obtain conditions under which these almost paracomplex structures are integrable, and the corresponding para-Kähler forms are symplectic. We also show that Petean's example of a nonflat indefinite Kähler-Einstein 4-manifold is a special case of our constructions. ...

3-submersions from QR-hypersurfaces of quaternionic Kähler manifolds

Gabriel Eduard Vîlcu (2010)

Annales Polonici Mathematici

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We study 3-submersions from a QR-hypersurface of a quaternionic Kähler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kähler manifolds which are not locally hyper-Kähler.

An extension theorem for Kähler currents with analytic singularities

Tristan C. Collins, Valentino Tosatti (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove an extension theorem for Kähler currents with analytic singularities in a Kähler class on a complex submanifold of a compact Kähler manifold.

Hartogs type extension theorems on some domains in Kähler manifolds

Takeo Ohsawa (2012)

Annales Polonici Mathematici

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Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact...