Estimate of the Einstein-Kähler metric on a weakly pseudoconvex domain in ℒ2

1996 ◽  
Vol 223 (3) ◽  
pp. 535-545 ◽  
Author(s):  
Wei Wang
Keyword(s):  
Pseudoconvex Domain ◽  
Kähler Metric ◽  
Weakly Pseudoconvex ◽  
Weakly Pseudoconvex Domain ◽  
Kahler Metric

scholarly journals SEMIGLOBAL EXTENSION OF MAXIMALLY COMPLEX SUBMANIFOLDS

2011 ◽  
Vol 84 (3) ◽  
pp. 458-474
Author(s):  
GIUSEPPE DELLA SALA ◽  
ALBERTO SARACCO
Keyword(s):  
Pseudoconvex Domain ◽  
Complex Submanifold ◽  
Weakly Pseudoconvex ◽  
Complex Variety ◽  
Complex Submanifolds ◽  
Weakly Pseudoconvex Domain ◽  
Analytic Sets

AbstractLet A be a domain of the boundary of a (weakly) pseudoconvex domain Ω of ℂn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain E of ℂn, depending only on Ω and A, and a complex variety W⊂E such that bW=M in E. Moreover, a generalization to analytic sets of depth at least 4 is given.

scholarly journals Toeplitz operators on certain weakly pseudoconvex domains

1981 ◽  
Vol 31 (1) ◽  
pp. 1-14 ◽  
Author(s):  
David Crocker ◽  
Iain Raeburn
Keyword(s):  
Hardy Space ◽  
Pseudoconvex Domain ◽  
Toeplitz Operators ◽  
Pseudoconvex Domains ◽  
Main Interest ◽  
Weakly Pseudoconvex ◽  
Weakly Pseudoconvex Domain ◽  
Continuous Symbol ◽  
Image Position ◽  
The Ideal

AbstractLet Ω be the weakly pseudoconvex domainand let ∂Ω be its boundary. If ϕ ∈ L∞ (∂Ω), we denote by Tϕ, the Toephtz operator with symbol ϕ acting on the Hardy space H2(∂Ω), and by J(∂Ω) the C*-subalgebra of B(H2(∂Ω)) generated by the Toeplitz operators with continuous symbol. Our main theorem asserts that J(∂Ω) contains the ideal K of all compact operators on H2(∂Ω), and that the symbol map ϕ→Tϕ induces an isomorphism of C(∂Ω) onto the quotient C*-algebra ℑ(∂Ω)/K. Similar results have been established before for other domains, and in particular when Ω is strongly pseudoconvex. The main interest of our results lies in their proofs: ours are elementary, whereas those used in the strongly pseudoconvex case depend heavily on the theory of the tangential Cauchy-Riemann operator.

scholarly journals Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
String Theory ◽  
Hierarchical Structure ◽  
Matter Field ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Kähler Metric ◽  
Yukawa Couplings ◽  
String Compactifications ◽  
Kahler Metric ◽  
Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

scholarly journals TWISTING OF N=1 SUSY GAUGE THEORIES AND HETEROTIC TOPOLOGICAL THEORIES

1995 ◽  
Vol 10 (30) ◽  
pp. 4325-4357 ◽  
Author(s):  
A. JOHANSEN
Keyword(s):  
Complex Structure ◽  
Kähler Manifold ◽  
Dolbeault Cohomology ◽  
Kähler Metric ◽  
Yang Mills ◽  
Kahler Manifold ◽  
Brst Charge ◽  
Kahler Metric ◽  
Compact Kähler Manifold ◽  
Topological Theories

It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.

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