Communications of the
Korean Mathematical Society CKMS

Let $(M^{2m},\varphi,g)$ be a $B$-manifold. In this paper, we introduce a new class of metric on $(M^{2m},\varphi,g)$, obtained by a non-conformal deformation of the metric $g$, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on $M$ with respect to a generalized Berger-type deformed metric.

Keywords: $B$-manifold, generalized Berger-type deformed metric, scalar curvature, biharmonic map

MSC numbers: Primary 53C20, 31B30, 53C43, 58E20