On $$L^{2}$$-Harmonic Forms of Complete Almost Kähler Manifold

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Teng Huang
Keyword(s):  
Kähler Manifold ◽  
Harmonic Forms ◽  
Kahler Manifold ◽  
Almost Kähler Manifold ◽  
Almost Kähler

A remark on an example of a 6-dimensional Einstein almost-Kähler manifold

2008 ◽  
Vol 88 (1-2) ◽  
pp. 70-74 ◽  
Author(s):  
Keiichiro Hirobe ◽  
Takashi Oguro ◽  
Kouei Sekigawa
Keyword(s):  
Kähler Manifold ◽  
Kahler Manifold ◽  
Almost Kähler Manifold ◽  
Almost Kähler

scholarly journals New Geometric Interpretation of Quaternionic Fueter Functions

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Wiesław Królikowski
Keyword(s):  
Kähler Manifold ◽  
Geometric Interpretation ◽  
Regular Functions ◽  
Kahler Manifold ◽  
Almost Kähler Manifold ◽  
Almost Kähler

AbstractA correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kähler manifold is shown.

scholarly journals On some compact almost Kähler locally symmetric space

1998 ◽  
Vol 21 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Takashi Oguro
Keyword(s):  
Symmetric Space ◽  
Scalar Curvature ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Symmetric Space ◽  
Kahler Manifold ◽  
Almost Kähler

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric spaceMis a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, thenMis a Kähler manifold.

scholarly journals On second non-HLC degree of closed symplecitc manifold

2021 ◽  
pp. 2150079
Author(s):  
Teng Huang
Keyword(s):  
Complex Structure ◽  
The Self ◽  
Almost Complex Structure ◽  
Harmonic Forms ◽  
Almost Complex ◽  
Almost Kähler Manifold ◽  
De Rham ◽  
Number Formula ◽  
Almost Kähler ◽  
Structure Formula

In this note, we show that for a closed almost-Kähler manifold [Formula: see text] with the almost complex structure [Formula: see text] satisfies [Formula: see text] the space of de Rham harmonic forms is contained in the space of symplectic-Bott–Chern harmonic forms. In particular, suppose that [Formula: see text] is four-dimensional, if the self-dual Betti number [Formula: see text], then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott–Chern harmonic forms.

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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