A new class of Riemannian metrics on tangent bundle of a Riemannian manifold
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1255-1267 https://doi.org/10.4134/CKMS.c200114 Published online August 28, 2020 Printed October 31, 2020
Amir Baghban, Saeed Hashemi Sababe Azarbaijan Shahid Madani University; Malard Branch, Islamic Azad University
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
