Lelong–Poincaré formula in symplectic and almost complex geometry

2020 ◽  
Vol 38 (3) ◽  
pp. 337-364
Author(s):  
Emmanuel Mazzilli ◽  
Alexandre Sukhov
Keyword(s):  
Complex Geometry ◽  
Almost Complex ◽  
Poincaré Formula

scholarly journals Conjugate connections with respect to a quadratic endomorphism and duality

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2367-2374 ◽  
Author(s):  
Cornelia-Livia Bejan ◽  
Mircea Crasmareanu
Keyword(s):  
Complex Geometry ◽  
Linear Connection ◽  
Main Interest ◽  
Conjugate Connections ◽  
Almost Complex ◽  
Conjugate Connection ◽  
Exponential Case

The goal of this paper is to consider the notion of conjugate connection in a unifying setting for both almost complex and almost product geometries, having as model the works of Mileva Prvanovic. A main interest is in finding classes of conjugate connections in duality with the initial linear connection; for example in the exponential case of almost complex geometry we arrive at a rule of quantization.

Mini-Workshop: Almost Complex Geometry

2021 ◽  
Vol 17 (4) ◽  
pp. 1657-1691
Author(s):  
Daniele Angella ◽  
Joana Cirici ◽  
Jean-Pierre Demailly ◽  
Scott Wilson
Keyword(s):  
Complex Geometry ◽  
Almost Complex

scholarly journals GENERALIZED COMPLEX GEOMETRY AND THE POISSON SIGMA MODEL

2005 ◽  
Vol 20 (13) ◽  
pp. 985-995 ◽  
Author(s):  
L. BERGAMIN
Keyword(s):  
Sigma Model ◽  
Complex Geometry ◽  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Poisson Structures ◽  
Generalized Complex Structures ◽  
Almost Complex ◽  
Generalized Complex ◽  
Poisson Sigma Model

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N = (2, 1) or N = (2, 2) supersymmetry, but a certain relation among the different Poisson structures is needed. Moreover, important relations of an additional almost complex structure are found, which have no immediate interpretation in terms of generalized complex structures.

scholarly journals Castelnuovo's bound and rigidity in almost complex geometry

2021 ◽  
Vol 379 ◽  
pp. 107550
Author(s):  
Aleksander Doan ◽  
Thomas Walpuski
Keyword(s):  
Complex Geometry ◽  
Almost Complex

Twist, elementary deformation and K/K correspondence in generalized geometry

2020 ◽  
Vol 31 (10) ◽  
pp. 2050078
Author(s):  
Vicente Cortés ◽  
Liana David
Keyword(s):  
Complex Geometry ◽  
Killing Vector ◽  
Kähler Manifold ◽  
Conformal Change ◽  
Kahler Manifold ◽  
Hirzebruch Surfaces ◽  
Almost Complex ◽  
Generalized Geometry ◽  
Twist Construction ◽  
Hermitian Structures

We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold [Formula: see text] with a Hamiltonian Killing vector field a new generalized Kähler manifold, depending on the choice of a pair of non-vanishing functions and compatible twist data. We study this construction when [Formula: see text] is toric, with emphasis on the four-dimensional case, and we apply it to deformations of the standard flat Kähler metric on [Formula: see text], the Fubini–Study metric on [Formula: see text] and the admissible Kähler metrics on Hirzebruch surfaces. As a further application, we recover the K/K (Kähler/Kähler) correspondence, by specializing to ordinary Kähler manifolds.

scholarly journals The complex geometry of two exceptional flag manifolds

2020 ◽  
Vol 199 (6) ◽  
pp. 2227-2241
Author(s):  
D. Kotschick ◽  
D. K. Thung
Keyword(s):  
Lie Group ◽  
Complex Geometry ◽  
Complex Structure ◽  
The Other ◽  
Flag Manifolds ◽  
Dimensional Sphere ◽  
Complex Structures ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Chern Numbers

Abstract We discuss the complex geometry of two complex five-dimensional Kähler manifolds which are homogeneous under the exceptional Lie group $$G_2$$ G 2 . For one of these manifolds, rigidity of the complex structure among all Kählerian complex structures was proved by Brieskorn; for the other one, we prove it here. We relate the Kähler assumption in Brieskorn’s theorem to the question of existence of a complex structure on the six-dimensional sphere, and we compute the Chern numbers of all $$G_2$$ G 2 -invariant almost complex structures on these manifolds.

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