A New Geometric Structure on Tangent Bundles

Authors

Nikos Georgiou, Department of Mathematics, Waterford Institute of Technology, Waterford, Co. Waterford, IrelandFollow
Brendan Guilfoyle, School of STEM, Munster Technological University, Kerry, Tralee, Co. Kerry, IrelandFollow

ORCID

0000-0002-7437-5046

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Mathematics | Physical Sciences and Mathematics | Physics

Publication Details

Journal of Geometry and Physics, vol. 172.

Abstract

For a Riemannian manifold (N, g), we construct a scalar flat neutral metric G on the tangent bundle TN. The metric is locally conformally flat if and only if either N is a 2- dimensional manifold or (N, g) is a real space form. It is also shown that G is locally symmetric if and only if g is locally symmetric. We then study submanifolds in TN and, in particular, find the conditions for a curve to be geodesic. The conditions for a Lagrangian graph in the tangent bundle TN to have parallel mean curvature are studied. Finally, using the cross product in R3 we show that the space of oriented lines in R3 can be minimally isometrically embedded in TR3

Recommended Citation

Nikos Georgiou, Brendan Guilfoyle, A new geometric structure on tangent bundles, Journal of Geometry and Physics, Volume 172, 2022, 104415, ISSN 0393-0440, https://doi.org/10.1016/j.geomphys.2021.104415