Abstract
We consider the unit tangent sphere bundle T1M of a Riemannian manifold (M, g) equipped with the canonical contact metric structure \({(\eta, \xi, \phi, \bar{g})}\) . We study the geometric properties of the base manifold M under the assumption that the trace of the Jacobi operator with respect to the characteristic vector field ξ is constant. Moreover, we give examples of Einstein Riemannian manifolds, other than rank one symmetric spaces or globally Ossermann manifolds, the unit tangent sphere bundles of which have constant trace of the Jacobi operator. Finally, we extend our main results to the tangent sphere bundle TrM of constant radius r > 0.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.