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 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.c210207Published online July 5, 2022Printed 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. Downloads: Full-text PDF   Full-text HTML

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