A note about a covariant derivative of a harmonic vector field in a Riemannian manifold


Nevena Pušić




Betti numbers are related to the topology of the manifold. The one-dimensional Betti number is equal to the number of linearly independent harmonic vector fields on the manifold. Every harmonic vector field is a gradient vector field. Using that fact, we are getting some results about covariant derivative of a harmonic vector field.