Isometric immersions from a Kähler manifold into the quaternionic projective space

2016 ◽  
Vol 151 (1-2) ◽  
pp. 243-254
Author(s):  
M. J. Ferreira ◽  
B. A. Simões ◽  
R. Tribuzy
Keyword(s):  
Projective Space ◽  
Kähler Manifold ◽  
Isometric Immersions ◽  
Quaternionic Projective Space ◽  
Kahler Manifold

scholarly journals Strongly not relatives Kähler manifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Michela Zedda
Keyword(s):  
Projective Space ◽  
Positive Constant ◽  
Complex Projective Space ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Infinite Dimensional ◽  
Kahler Manifold ◽  
Hartogs Domains ◽  
Complex Projective

Abstract 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 the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.

Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space

2020 ◽  
Vol 70 (4) ◽  
pp. 863-876
Author(s):  
Ha Huong Giang
Keyword(s):  
Projective Space ◽  
General Condition ◽  
General Position ◽  
Kähler Manifold ◽  
Uniqueness Problem ◽  
Uniqueness Theorems ◽  
Meromorphic Mappings ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

AbstractIn this article, we prove a new generalization of uniqueness theorems for meromorphic mappings of a complete Kähler manifold M into ℙn(ℂ) sharing hyperplanes in general position with a general condition on the intersections of the inverse images of these hyperplanes.

scholarly journals Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds

2021 ◽  
Author(s):  
Fedor Bogomolov ◽  
Nikon Kurnosov ◽  
Alexandra Kuznetsova ◽  
Egor Yasinsky
Keyword(s):  
Automorphism Group ◽  
Projective Space ◽  
Kähler Manifold ◽  
Symplectic Manifolds ◽  
Finite Degree ◽  
Partial Classification ◽  
Kahler Manifold ◽  
Degeneracy Locus ◽  
Algebraic Reduction

Abstract We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works by D. Guan and the 1st author. Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$ cover of some non-Kähler manifold $W_F$, which we call the base of $Q$. We show that the algebraic reduction of $Q$ and its base is the projective space of dimension $n-1$. Besides, we give a partial classification of submanifolds in $Q$, describe the degeneracy locus of its algebraic reduction and prove that the automorphism group of $Q$ satisfies the Jordan property.

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

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