Some special vector fields and their dual fields

A vector field defined by Finn in n-dimensional Euclidean space (n greater than or equal to 2) over domain Omega of a capillary surface S, is expressed by means of the elements of the surface Sigma which is the boundary of Omega. The importance of this vector field is that it characterizes by itself the necessary and sufficient conditions for the existence and boundary value problems of the capillary surfaces. The aim of this paper is to determine some necessary and sufficient conditions for the related vector fields of capillary surfaces to be Killing and Harmonic vectors and to extend the concept of dual field to hypersurfaces of odd dimensional Euclidean space.