The vector space of conformal Killing forms on a Riemannian manifold
\textit{T. Kashiwada} [Natur. Sci. Rep. Ochanomizu Univ. 19, 67-74 (1968; Zbl 0179.26902)] and \textit{S. Tachibana} [Tohoku Math. J. (2) 21, 56-64 (1969; Zbl 0182.55301)], defined conformal Killing \(p\)-forms on a Riemanian manifold of dimension \(m>p\geq 1\) and generalized some results on conformal Killing vector fields to the case of such forms. In this paper the author's investigations [in Tensor, New Ser. 58, 233-242 (1997; Zbl 0954.53026)] are continued and developed. The author defines conformal Killing \(p\)-forms with the help of natural differential operators on Riemannian manifolds [\textit{E. Looijenga} and \textit{V. A. Lunts}, Invent. Math. 129, 361-412 (1997; Zbl 0890.53030)], and representations of orthogonal groups. The geometry of the vector space \({\mathbf T}^p(M,R)\) of conformal Killing \(p\)-forms and of its two subspaces \({\mathbf K}^p(M,R)\) of coclosed conformal Killing \(p\)-forms and \({\mathbf P}^p(M,R)\) of closed conformal Killing \(p\)-forms are considered. Some local and global results due to S. Tachibana and T. Kashiwada about conformal Killing and Killing \(p\)-forms are generalized. An application to Hermitian geometry is given.
scientific article; zbMATH DE number 1777783