Para-HyperKa<spacing diaeresis>hler Geometry of the Deformation Space of Maximal Globally Hyperbolic Anti-de Sitter Three-Manifolds

被引：0
作者：
Mazzoli, Filippo [1 ]
Seppi, Andrea [2 ]
Tamburelli, Andrea [3 ]
机构：
[1] Univ Calif Riverside, Dept Math, 900 Univ Ave,Skye Hall 378, Riverside, CA 92521 USA
[2] Univ Torino, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy
[3] Univ Pisa, Dept Math, Largo Bruno Pontecorvo 5, I-56124 Pisa, Italy
来源：
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 306卷 / 1546期
基金：
美国国家科学基金会;
关键词：
HARMONIC MAPS; SYMPLECTIC-GEOMETRY; CYCLIC EXTENSION; WICK ROTATIONS; SURFACES; CURVATURE; ENERGY; DEGENERATION; EQUATIONS;
D O I：
10.1090/memo/1546
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the para-hyper-K & auml;hler geometry of the deformation space of MGHC anti-de Sitter structures on Sigma R, for Sigma a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three symplectic structures coexist with an integrable complex structure and two para-complex structures, satisfying the relations of para-quaternionic numbers. We show that these structures are directly related to the geometry of MGHC manifolds, via the Mess homeomorphism, the parameterization of Krasnov-Schlenker by the induced metric on K-surfaces, the identification with the cotangent bundle T & ring;T(Sigma), and the circle action that arises from this identification. Finally, we study the relation to the natural para-complex geometry that the space inherits from being a component of the PSL(2, B)-character variety, where B is the algebra of para-complex numbers, and the symplectic geometry deriving from Goldman symplectic form.
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页码：1 / 107
页数：120
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