scholarly journals Construction of projective special Kähler manifolds

2021 ◽  
Author(s):  
Mauro Mantegazza
Keyword(s):  
Lie Groups ◽  
Symmetric Tensor ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Structure ◽  
Special Kähler Manifolds

AbstractIn this paper, we present an intrinsic characterisation of projective special Kähler manifolds in terms of a symmetric tensor satisfying certain differential and algebraic conditions. We show that this tensor vanishes precisely when the structure is locally isomorphic to a standard projective special Kähler structure on $$\mathrm {SU}(n,1)/\mathrm {S}(\mathrm {U}(n)\mathrm {U}(1))$$ SU ( n , 1 ) / S ( U ( n ) U ( 1 ) ) . We use this characterisation to classify 4-dimensional projective special Kähler Lie groups.

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

2006 ◽  
Vol 84 (10) ◽  
pp. 891-904
Author(s):  
J R Schmidt
Keyword(s):  
Coordinate System ◽  
Lie Groups ◽  
Lie Algebra ◽  
Poisson Structure ◽  
Kähler Manifolds ◽  
Coadjoint Orbits ◽  
Kahler Manifolds ◽  
Canonical Transformations ◽  
Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

scholarly journals A note on special Kähler manifolds

1999 ◽  
Vol 313 (4) ◽  
pp. 711-713 ◽  
Author(s):  
Zhiqin Lu
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Special Kähler Manifolds

scholarly journals Quaternionic Kähler metrics associated with special Kähler manifolds

2015 ◽  
Vol 92 ◽  
pp. 271-287 ◽  
Author(s):  
D.V. Alekseevsky ◽  
V. Cortés ◽  
M. Dyckmanns ◽  
T. Mohaupt
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Special Kähler Manifolds ◽  
Quaternionic Kähler

scholarly journals THE BATALIN-VILKOVISKY FORMALISM ON FERMIONIC KÄHLER MANIFOLDS

1993 ◽  
Vol 08 (39) ◽  
pp. 3773-3784 ◽  
Author(s):  
S. AOYAMA ◽  
S. VANDOREN
Keyword(s):  
Phase Space ◽  
Symmetric Space ◽  
Master Equation ◽  
Kähler Manifold ◽  
Hermitian Symmetric Space ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kähler Structure ◽  
Kahler Manifold

We show that the Kähler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kähler manifold. By introducing an isometry we explicitly construct the fermionic irreducible hermitian symmetric space. We then give some solutions of the master equation in the BV formalism.

Holomorphically projective mappings of special Kähler manifolds

2018 ◽  
Author(s):  
V. Kiosak ◽  
A. Savchenko ◽  
T. Shevchenko
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Special Kähler Manifolds
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