# On the geometry of frame bundles

## Kamil Niedziałomski

Address: Department of Mathematics and Computer Science, University of Łódź, ul. Banacha 22, 90–238 Łódź, Poland

E-mail: kamiln@math.uni.lodz.pl

Abstract: Let $(M,g)$ be a Riemannian manifold, $L(M)$ its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle $TM$. We compute the Levi–Civita connection and curvatures of these metrics.

AMSclassification: primary 53C10; secondary 53C24, 53A30.

Keywords: Riemannian manifold, frame bundle, tangent bundle, natural metric.

DOI: 10.5817/AM2012-3-197