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

Abstract

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.

Keywords

• Cheeger-Gromoll type deformation of metric g
• Riemannian curvature
• harmonic maps
• biharmonic maps

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