Some Properties Concerning the Cheeger-Gromoll Type Deformation of Metric $g$ on a Riemannian Manifold $(M^{m},g)$

In this paper, we introduce a new class of metrics on a Riemannian manifold, which is obtained by deforming the metric of this Riemannian manifold into a Cheeger-Gromoll-type metric. We first investigate the Levi-Civita connection for this metric. Then we characterize the Riemannian curvature, the sectional curvature, and the scalar curvature. Finally, we explore a class of harmonic and biharmonic maps.