A Note on Geodesic Vector Fields

Abstract

The concircularity property of vector fields implies the geodesicity property, while the converse of this statement is not true. The main objective of this note is to find conditions under which the concircularity and geodesicity properties of vector fields are equivalent. Moreover, it is shown that the geodesicity property of vector fields is also useful in characterizing not only spheres, but also Euclidean spaces.

Keywords

• geodesic vector field
• concircular vector field
• n-sphere
• Euclidean space