Communications of the
Korean Mathematical Society CKMS

Let $(M^{m},g)$ be an $m$-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on $(M^{m},g)$, obtained by a non-conformal deformation of the metric $g$. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when $(M^{m}, g)$ is an Euclidean space.

Keywords: Riemannian manifold, semi-conformal deformation of metric, scalar curvature, biharmonic map

MSC numbers: Primary 53C20, 55B05, 53C05

Supported by: This work was supported by PRFU and LGACA Saida Laboratory.