Sasakian-Einstein structures on 9#(S2 x S3)

被引：22

作者：

Boyer, CP ^{[1
]}

Galicki, K ^{[1
]}

Nakamaye, M ^{[1
]}

机构：

[1] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 354卷 / 08期

关键词：

D O I：

10.1090/S0002-9947-02-03015-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that 9#(S(2)xS(3)) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound b(2) (M) less than or equal to 8 which holds for any regular Sasakian-Einstein M does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and describe the orbifold version.

引用

页码：2983 / 2996

页数：14

共 25 条

[1]

Bando S., 1987, Adv. Stud. Pure Math., V10, P11

[2]

Besse A.L., 1987, EINSTEIN MANIFOLDS

[3] Chern classes and Hirzebruch-Riemann-Roch theorem for coherent sheaves on complex-projective orbifolds with isolated singularities [J].

Blache, R .

MATHEMATISCHE ZEITSCHRIFT, 1996, 222 (01) :7-57

[4]

Boyer C, 1999, J DIFFER GEOM, P123

[5]

Boyer CP, 2001, J DIFFER GEOM, V57, P443

[6] On Sasakian-Einstein geometry [J].

Boyer, CP ;

Galicki, K .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2000, 11 (07) :873-909

[7]

BOYER CP, MATHDG0104126

[8]

BOYER CP, MATHDG0012047

[9] Semi-continuity of complex singularity exponents and Kahler-Einstein metrics on Fano orbifolds [J].

Demailly, JP ;

Kollár, J .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2001, 34 (04) :525-556

[10]

DOLGACHEV I, 1982, LECT NOTES MATH, V956, P34

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