Curvatures of the diagonal lift from an affine manifold to the linear frame bundle

Abstract

We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A.

Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold.

We receive analogous and, surprisingly, even stronger results in our affine setting.

Keywords

• Riemannian manifold
• linear frame bundle
• natural metric
• affine connection
• Sasaki-Mok metric