On the nonexistence of Einstein metrics on 4-manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Sung, Chanyoung^1,2 

[1] Konkuk Univ, Dept Math, Seoul, South Korea

[2] Konkuk Univ, Inst Math Sci, Seoul, South Korea

关键词: Einstein metric;    Seiberg-Witten theory;   

DOI  :  10.1016/j.geomphys.2010.12.002

来源: Elsevier

【 摘 要 】

By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metrics on manifolds obtained from a 4-manifold with a nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or appropriate surgeries along circles or homologically trivial 2-spheres with closed oriented 4-manifolds with negative-definite intersection form. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free