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

نویسندگان
Mirzaie, Reza ID 1
Vatandoost, Ebrahim ID 2
Heidarkhani Gilani, Shiva ID 3

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

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

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

doi
10.22060/ajmc.2023.22527.1165
چکیده

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

کلیدواژه‌ها
Metric dimension, Riemannian manifold, Graph