@article{Ishan2023, 
author = {Amira Ishan},
title = {On concurrent vector fields on Riemannian manifolds},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {25097-25103},
keywords = {concurrent vector fields, Euclidean spaces, de-Rham Laplace operator, Ricci curvature},
url = {https://www.sciopen.com/article/10.3934/math.20231281},
doi = {10.3934/math.20231281},
abstract = {It is shown that the presence of a non-zero concurrent vector field on a Riemannian manifold poses an obstruction to its topology as well as certain aspects of its geometry. It is shown that on a compact Riemannian manifold, there does not exist a non-zero concurrent vector field. Also, it is shown that a Riemannian manifold of non-zero constant scalar curvature does not admit a non-zero concurrent vector field. It is also shown that a non-zero concurrent vector field annihilates de-Rham Laplace operator. Finally, we find a characterization of a Euclidean space using a non-zero concurrent vector field on a complete and connected Riemannian manifold.}
}