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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0033-7,
author = {Old\v rich Kowalski and Masami Sekizawa},
title = {Curvatures of the diagonal lift from an affine manifold to the linear frame bundle},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {837-843},
zbl = {1262.53021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0033-7}
}
Oldřich Kowalski; Masami Sekizawa. Curvatures of the diagonal lift from an affine manifold to the linear frame bundle. Open Mathematics, Tome 10 (2012) pp. 837-843. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0033-7/
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