Tensor sphere bundle of Cheeger-Gromoll type

TL;DR

This paper constructs an almost metrical paracontact structure on the tensor sphere bundle of a Riemannian manifold with a Cheeger-Gromoll type metric, revealing it is not a space form.

Contribution

It introduces a new geometric structure on tensor sphere bundles with Cheeger-Gromoll metrics, expanding understanding of their properties.

Findings

Tensor sphere bundles with the induced metric are never space forms.

An almost metrical paracontact structure is established on these bundles.

The construction provides new insights into the geometry of tensor bundles.

Abstract

We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundles endowed with the induced metric are never space forms.