New methods of the Bochner technique and their applications (Q1866707)

The Bochner technique is a general method for proving vanishing theorems. The purpose of this paper is to extend the field of application. The author uses the Bochner technique to obtain some theorems in affine differential geometry and tensor bundle geometry over a manifold. In particular, he proves that \(T^p(M,R)\cong T^{n-p}(M,R)\) for an \(n\)-dimensional Riemannian manifold \((M,g)\), where \(T^p(M,R)\) denotes the vector space of conformal Killing \(p\)-forms on \((M,g)\).