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http://dx.doi.org/10.4134/CKMS.c210207

SOME RESULTS ON THE GEOMETRY OF A NON-CONFORMAL DEFORMATION OF A METRIC  

Djaa, Nour Elhouda (Department of Applied Mathematics Relizane University)
Zagane, Abderrahim (Department of Mathematics Relizane University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 865-879 More about this Journal
Abstract
Let (Mm, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (Mm, 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 (Mm, g) is an Euclidean space.
Keywords
Riemannian manifold; semi-conformal deformation of metric; scalar curvature; biharmonic map;
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