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 R-3 we show that the space of oriented lines in R-3 can be minimally isometrically embedded in TR3. (C) 2021 The Authors. Published by Elsevier B.V.
Almost para Kaehler structureTangent bundleNeutral metricSPACE
NSTL
Elsevier
