The sectional curvature of the tangent bundles with general natural lifted metrics.(English)Zbl 1192.53033

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 198-209 (2008).
Summary: We study some properties of the tangent bundles with metrics of general natural lifted type. We consider a Riemannian manifold $$(M,g)$$ and we find the conditions under which the Riemannian manifold $$(TM,G)$$, where $$TM$$ is the tangent bundle of $$M$$ and $$G$$ is the so-called general natural lifted metric of $$g$$, has constant sectional curvature.
For the entire collection see [Zbl 1154.17001].

MSC:

 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C20 Global Riemannian geometry, including pinching
Full Text: