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On the Burns-Epstein invariants of spherical CR 3-manifolds

Khoi The Vu (2011)

Annales de l’institut Fourier

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.

On the Calabi-Yau equation in the Kodaira-Thurston manifold

Luigi Vezzoni (2016)

Complex Manifolds

We review some previous results about the Calabi-Yau equation on the Kodaira-Thurston manifold equipped with an invariant almost-Kähler structure and assuming the volume form T2-invariant. In particular, we observe that under some restrictions the problem is reduced to aMonge-Ampère equation by using the ansatz ˜~ω = Ω− dJdu + da, where u is a T2-invariant function and a is a 1-form depending on u. Furthermore, we extend our analysis to non-invariant almost-complex structures by considering some...

On the embedding and compactification of q -complete manifolds

Ionuţ Chiose (2006)

Annales de l’institut Fourier

We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form N N - q . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as X ¯ ( X ¯ N - q ) where X ¯ N is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into 1 × N .

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that ̅ ω k = 0 for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K X - 1 is nef, then for any ε >...

On weighted Bergman kernels of bounded domains

Sorin Dragomir (1994)

Studia Mathematica

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains Ω N for admissible weights a L ¹ ( Ω ) .

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