A new class of Riemannian metrics on tangent bundle of a Riemannian manifold
Commun. Korean Math. Soc.
Published online August 28, 2020
Amir Baghban and Saeed Hashemi Sababe
Facultu of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran, Department of Mathematical and Statistical Sciences, University of Alberta
Abstract : The class of isotropic almost complex structures, $J_{\delta , \sigma}$, define a class of Riemannian metrics, $g_{\delta , \sigma}$, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics $g_{\delta , 0}$ using the geometry of tangent bundle. As a by-product, some integrability results will be reported for $J_{\delta , \sigma}$.
Keywords : Einstein manifold, isotropic almost complex structure, integrability, space form, tangent bundle
MSC numbers : 53C25, 53C15
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