Some results on the geometry of a non-conformal deformation of a metric
Commun. Korean Math. Soc. 2022 Vol. 37, No. 3, 865-879
https://doi.org/10.4134/CKMS.c210207
Published online July 5, 2022
Printed July 31, 2022
Nour Elhouda Djaa, Abderrahim Zagane
Relizane University; Relizane University
Abstract : 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.
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