Convex real projective structures and Weil's local rigidity theorem

被引：0

作者：

Kim, Inkang ^{[1
]}

Zhang, Genkai ^{[2
]}

机构：

[1] KIAS, Sch Math, Heogiro 85, Seoul 130722, South Korea

[2] Gothenburg Univ, Chalmers Univ Technol & Math Sci, Math Sci, SE-41296 Gothenburg, Sweden

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 116卷

关键词：

Zariski tangent space; Real projective structure; Weil's local rigidity; LIE-GROUPS; SURFACES; SPACE;

D O I：

10.1016/j.matpur.2018.06.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an n-dimensional real hyperbolic manifold M, we calculate the Zariski tangent space of a character variety chi(pi(1)(M), SL(n +1, R), n > 2 at Fuchsian locus to show that the tangent space consists of cubic forms. Furthermore we prove the Weil's local rigidity theorem for uniform hyperbolic lattices using real projective structures. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：40 / 51

页数：12

共 14 条

[1] Convexes divisibles III [J].

Benoist, Y .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2005, 38 (05) :793-832

[2] Automorphisms of convex cones [J].

Benoist, Y .

INVENTIONES MATHEMATICAE, 2000, 141 (01) :149-193

[3] CONVEX REAL PROJECTIVE-STRUCTURES ON CLOSED SURFACES ARE CLOSED [J].

CHOI, S ;

GOLDMAN, WM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (02) :657-661

[4]

Eichler M., 1957, MATH Z, V67, P267, DOI [10.1007/BF01258863, DOI 10.1007/BF01258863]

[5] LIE-GROUPS AND TEICHMULLER SPACE [J].

HITCHIN, NJ .

TOPOLOGY, 1992, 31 (03) :449-473

[6]

Johnson Dennis, 1987, PROGR MATH, V67, P48, DOI [10.1007/978-1-4899-6664-3_3, 10.1007/978-1-4899-6664-3]

[7] Eichler-Shimura isomorphism for complex hyperbolic lattices [J].

Kim, Inkang ;

Zhang, Genkai .

JOURNAL OF GEOMETRY AND PHYSICS, 2017, 121 :452-460

[8] KAHLER METRIC ON THE SPACE OF CONVEX REAL PROJECTIVE STRUCTURES ON SURFACE [J].

Kim, Inkang ;

Zhang, Genkai .

JOURNAL OF DIFFERENTIAL GEOMETRY, 2017, 106 (01) :127-137

[9]

Kim I, 2010, J DIFFER GEOM, V86, P189

[10]

Labourie F, 2007, PURE APPL MATH Q, V3, P1057

← 1 2 →