Conformally-projectively flat statistical structures on tangent bundles over statistical manifolds. (English) Zbl 1194.53015
Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007, Olomouc, Czech Republic, August 27–31, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-279-060-6/hbk). 239-251 (2008).
Authors’ abstract: Let \((M, h,\nabla)\) be a statistical manifold of dimension \(n\geq2\). We show that \((M,h,\nabla)\) is of constant curvature if and only if the tangent bundle \(T M\) over \(M\) with complete lift statistical structure \((h^C,\nabla^C)\) is conformally-projectively flat.
For the entire collection see [Zbl 1154.53003].
For the entire collection see [Zbl 1154.53003].
MSC:
| 53B05 | Linear and affine connections |
| 53B20 | Local Riemannian geometry |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
