scholarly journals A formally Kähler structure on a knot space of a G 2-manifold

2011 ◽  
Vol 18 (3) ◽  
pp. 539-555
Author(s):  
Misha Verbitsky
Keyword(s):  
Kähler Structure ◽  
Knot Space

scholarly journals Yang–Mills connections on compact complex tori

2015 ◽  
Vol 07 (02) ◽  
pp. 293-307
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Structure Group ◽  
Kähler Structure ◽  
Yang Mills ◽  
Complex Torus ◽  
Complex Tori

Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the underlying principal G-bundle EG is semistable (respectively, polystable).

scholarly journals Almost Complex Surfaces in the Nearly Kähler SL(2,ℝ) × SL(2,ℝ)

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1160
Author(s):  
Elsa Ghandour ◽  
Luc Vrancken
Keyword(s):  
Complete Classification ◽  
Second Fundamental Form ◽  
Complex Surfaces ◽  
Kähler Structure ◽  
Totally Geodesic ◽  
Parallel Second Fundamental Form ◽  
Almost Complex ◽  
Nearly Kähler ◽  
Nearly Kähler Structure

The space S L ( 2 , R ) × S L ( 2 , R ) admits a natural homogeneous pseudo-Riemannian nearly Kähler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.

The Poincaré Dual of a Geodesic Algebraic Curve in a Quotient of the 2-Ball

1981 ◽  
Vol 33 (2) ◽  
pp. 485-499 ◽  
Author(s):  
Stephen S. Kudla ◽  
John J. Millson
Keyword(s):  
Algebraic Curve ◽  
Inverse Image ◽  
Universal Covering ◽  
Explicit Construction ◽  
Holomorphic Curve ◽  
Volume Form ◽  
Harmonic Form ◽  
Bergman Metric ◽  
Kähler Structure ◽  
Totally Geodesic

We shall consider an irreducible, non-singular, totally geodesic holomorphic curve N in a compact quotient M = Γ\D of the unit ball D = {(z, w):|z|2 + |w|2 < 1} in C2 with the Kahler structure provided by the Bergman metric. The main result of this paper is an explicit construction of the harmonic form of type (1,1) which is dual to N. Our construction is as follows. Let p:D → Γ\D be the universal covering map. Choose a component D1 in the inverse image of N under p. The choice of D1 corresponds to choosing an embedding of the fundamental group of N into Γ. We denote the image by Γ1. Let π : D → D1 be the fiber bundle obtained by exponentiating the normal bundle of D1 in D. Let μ be the volume form of D1.

scholarly journals Geometric viewpoint on the quantization of a fuzzy logic

2020 ◽  
Vol 17 (13) ◽  
pp. 2050201
Author(s):  
Davide Pastorello
Keyword(s):  
Fuzzy Logic ◽  
Phase Space ◽  
Complex Projective Space ◽  
Product Formula ◽  
Kähler Structure ◽  
Set Operations ◽  
Logical Connectives ◽  
Standard Set ◽  
Complex Projective ◽  
Geometric Formulation

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.

scholarly journals Local Models of Isolated Singularities for Affine Special Kähler Structures in Dimension Two

2018 ◽  
Vol 2020 (17) ◽  
pp. 5215-5235 ◽  
Author(s):  
Martin Callies ◽  
Andriy Haydys
Keyword(s):  
Local Models ◽  
Isolated Singularities ◽  
Kähler Structure ◽  
Real Dimension ◽  
Cubic Form ◽  
Kähler Structures ◽  
Symplectic Connection

Abstract We construct local models of isolated singularities for special Kähler structures in real dimension two assuming that the associated holomorphic cubic form does not have essential singularities. As an application we compute the holonomy of the flat symplectic connection, which is a part of the special Kähler structure.

scholarly journals Kähler structure in the commutative limit of matrix geometry

2016 ◽  
Vol 2016 (8) ◽  
Author(s):  
Goro Ishiki ◽  
Takaki Matsumoto ◽  
Hisayoshi Muraki
Keyword(s):  
Kähler Structure

scholarly journals The Bochner-flat cone of a CR manifold

2008 ◽  
Vol 144 (3) ◽  
pp. 747-773
Author(s):  
Liana David
Keyword(s):  
Open Subset ◽  
Kähler Manifold ◽  
Parameter Family ◽  
Local Geometry ◽  
Cr Manifold ◽  
Kähler Structure ◽  
Complex Dimension ◽  
Kahler Manifold ◽  
Pseudo Convex

AbstractWe construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a one-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two is locally isomorphic to a generalised Kähler cone.

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