A remark on the metric dimension in Riemannian manifolds of constant curvature

Document Type : Original Article

Authors

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

Abstract

We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weighted metric
dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G = (V,E)$ embedded in a Riemannin manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V| − 1$.

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Main Subjects