The Vector Space of Conformal Killing Forms on a Riemannian Manifold

Abstract

T. Kashiwada and S. Tachibana defined conformal Killing p-forms on a Riemannian manifold of dimension $$m > p \geqslant 1$$ and generalized some results on conformal Killing vector fields to the case of such forms. In this paper, conformal Killing p-forms are defined with the help of natural differental operators on Riemannian manifolds and representations of orthogonal groups. The geometry of the vector space $$T^p(M,\mathbb{R})$$ of conformal Killing p-forms and of its two subspaces $$T^p(M,\mathbb{R})$$ of coclosed conformal Killing p-forms and $$P^p(M,\mathbb{R})$$ of closed conformal Killing p-forms are considered. Some local and global results due to Tachibana and Kashiwada about conformal Killing and Killing p-forms are generalized. An application to Hermitian geometry is given. Bibliography: 30 titles.