Analysis and geometry on complex homogeneous domains, by Jacques Faraut, Soji Kaneyuki, Adam Korányi, Qi-keng Lu and Guy Roos. Progress in Mathematics 185. Pp. 540. SFr118. 2000. ISBN 3 7643 4138 6 (Birkhäuser). - Complex tori, by Christina Birkenhake and Herbert Lange. Progress in Mathematics 177. Pp. 251. SFr88. 1999. ISBN 3 7643 4103 3 (Birkhäuser).

2000 ◽  
Vol 84 (500) ◽  
pp. 381-381
Author(s):  
Steve Abbott
Keyword(s):  
Complex Tori ◽  
Homogeneous Domains

scholarly journals Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

2017 ◽  
Vol 21 (4) ◽  
pp. 2419-2460 ◽  
Author(s):  
Giuseppe Pareschi ◽  
Mihnea Popa ◽  
Christian Schnell
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Complex Tori ◽  
Generic Vanishing

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).

A Clifford algebra-based grand unification program of gravity and the Standard Model: a review study

2014 ◽  
Vol 92 (12) ◽  
pp. 1501-1527 ◽  
Author(s):  
Carlos Castro
Keyword(s):  
Standard Model ◽  
Geometric Probability ◽  
Coupling Constants ◽  
Grand Unified Theory ◽  
Neutrino Mixing ◽  
Yang Mills ◽  
Bounded Complex ◽  
The Standard Model ◽  
Mixing Matrix ◽  
Homogeneous Domains

A Clifford Cl(5, C) unified gauge field theory formulation of conformal gravity and U(4) × U(4) × U(4) Yang–Mills in 4D, is reviewed along with its implications for the Pati–Salam (PS) group SU(4) × SU(2)L × SU(2)R, and trinification grand unified theory models of three fermion generations based on the group SU(3)C × SU(3)L × SU(3)R. We proceed with a brief review of a unification program of 4D gravity and SU(3) × SU(2) × U(1) Yang–Mills emerging from 8D pure quaternionic gravity. A realization of E8 in terms of the Cl(16) = Cl(8) ⊗ Cl(8) generators follows, as a preamble to F. Smith’s E8 and Cl(16) = Cl(8) ⊗ Cl(8) unification model in 8D. The study of chiral fermions and instanton backgrounds in CP2 and CP3 related to the problem of obtaining three fermion generations is thoroughly studied. We continue with the evaluation of the coupling constants and particle masses based on the geometry of bounded complex homogeneous domains and geometric probability theory. An analysis of neutrino masses, Cabbibo–Kobayashi–Maskawa quark-mixing matrix parameters, and neutrino-mixing matrix parameters follows. We finalize with some concluding remarks about other proposals for the unification of gravity and the Standard Model, like string, M, and F theories and noncommutative and nonassociative geometry.

scholarly journals Examples of unbounded homogeneous domains in complex space

2005 ◽  
Vol 48 (S1) ◽  
pp. 248-261 ◽  
Author(s):  
Michael Eastwood ◽  
Alexander Isaev
Keyword(s):  
Complex Space ◽  
Homogeneous Domains

One-Dimensional Random Walk in Alternating Homogeneous Domains

1987 ◽  
Vol 47 (5) ◽  
pp. 1103-1111 ◽  
Author(s):  
Ora E. Percus ◽  
Jerome K. Percus
Keyword(s):  
Random Walk ◽  
One Dimensional ◽  
Homogeneous Domains

Analysis and Geometry on Complex Homogeneous Domains

2000 ◽  
Author(s):  
Jacques Faraut ◽  
Soji Kaneyuki ◽  
Adam Korányi ◽  
Qi-keng Lu ◽  
Guy Roos
Keyword(s):  
Homogeneous Domains

scholarly journals On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Romi F. Shamoyan ◽  
Olivera Mihić
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Siegel Domains ◽  
Type Spaces ◽  
Tube Type ◽  
Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

scholarly journals A characterization of compact complex tori via automorphism groups

2013 ◽  
Vol 357 (3) ◽  
pp. 961-968 ◽  
Author(s):  
Baohua Fu ◽  
De-Qi Zhang
Keyword(s):  
Automorphism Groups ◽  
Complex Tori
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