Abstract
The complete lift of a Riemannian metric g on a differentiable manifold M is not 0-homogeneous on the fibers of the tangent bundle TM. In this paper we introduce a new kind of lift G of g, which is 0-homogeneous. It determines a pseudo-Riemannian metric on \({\widetilde {TM}}\) , which depends only on the metric g. We obtain the Levi-Civita connection of this metric and study conformal vector fields on (\({\widetilde {TM},G}\)). Finally, we introduce the almost product and complex structures which preserve homogeneity and study certain geometrical properties of these structures.
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Peyghan, E., Heydari, A. & Razavi, A. The 0-Homogenous Complete Lift Metric. Mediterr. J. Math. 9, 693–707 (2012). https://doi.org/10.1007/s00009-011-0145-5
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DOI: https://doi.org/10.1007/s00009-011-0145-5