Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20231225A remark on the metric dimension in Riemannian manifolds of constant curvature532610.22060/ajmc.2023.22527.1165ENShivaHeidarkhani GilaniDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranRezaMirzaieDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranEbrahimVatandoostDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranJournal Article20230703We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weighted metric<br />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 $|V| − 1$.