Positive scalar curvature and the Euler class

JOURNAL OF GEOMETRY AND PHYSICS

卷:126

Article

Yu, Jianqing¹  Zhang, Weiping^2,3 

[1] Univ Sci & Technol China, Sch Math Sci, 96 Jinzhai Rd, Hefei 230026, Anhui, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Positive scalar curvature;    Flat vector bundle;    Euler class;   

DOI  :  10.1016/j.geomphys.2018.01.015

来源: Elsevier

【 摘 要 】

We prove the following generalization of the classical Lichnerowicz vanishing theorem: if F is an oriented flat vector bundle over a closed spin manifold M such that TM carries a metric of positive scalar curvature, then <(A) over cap (TM)e(F), [M]> = 0, where e(F) is the Euler class of F. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free