The Vranceanu Connections on The Riemannian (1, 1)-Tensor Bundle

摘要

The present paper deals with Vranceanu connections associated with the Levi-Civita connections of the Sasaki type and Cheeger-Gromoll type metrics on the (1, 1)-tensor bundle. Because of coinciding the Vranceanu connection associated with the Levi-Civita connection of the Sasaki type metric and the horizontal lift of the Levi-Civita connection of the base manifold's metric, we focus especially on the Vranceanu connection associated with the Levi-Civita connection of the Cheeger-Gromoll type metric.