On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

JOURNAL OF GEOMETRY AND PHYSICS

卷:111

Article

Arnlind, Joakim¹  Wilson, Mitsuru² 

[1] Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden

[2] Univ Western Ontario, Middlesex Coll, London, ON N6A 5B7, Canada

关键词: Noncommutative differential geometry;    Chern-Gauss-Bonnet theorem;    Levi-Civita connection;    Riemannian curvature;    Noncommutative 4-sphere;   

DOI  :  10.1016/j.geomphys.2016.10.016

来源: Elsevier

【 摘 要 】

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free