Symmetric spaces, Kähler geometry and Hamiltonian dynamics

1999 ◽  
pp. 13-33 ◽  
Author(s):  
S. K. Donaldson
Keyword(s):  
Symmetric Spaces ◽  
Hamiltonian Dynamics ◽  
Kahler Geometry

scholarly journals CHARGE ORBITS OF SYMMETRIC SPECIAL GEOMETRIES AND ATTRACTORS

2006 ◽  
Vol 21 (25) ◽  
pp. 5043-5097 ◽  
Author(s):  
STEFANO BELLUCCI ◽  
SERGIO FERRARA ◽  
MURAT GÜNAYDIN ◽  
ALESSIO MARRANI
Keyword(s):  
Black Hole ◽  
Critical Points ◽  
Symmetric Spaces ◽  
Central Charge ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Extremal Black Hole ◽  
Kahler Geometry ◽  
Complex Scalar ◽  
Black Hole Background

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to nV vector multiplets, in an asymptotically flat extremal black hole background described by a 2(nV+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein–Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(nV+1)-dimensional representation RV of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing quartic invariant (for rank-3 spaces). Other than the ½-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

Mean ergodic theorem in function symmetric spaces for infinite measure

2018 ◽  
Vol 2018 (1) ◽  
pp. 35-46
Author(s):  
Vladimir Chilin ◽  
◽  
Aleksandr Veksler ◽  
Keyword(s):  
Ergodic Theorem ◽  
Symmetric Spaces ◽  
Infinite Measure ◽  
Mean Ergodic Theorem

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

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