Projective functional tensors and other allied functionals

Abstract

Introduction. - Some time ago I discovered a sequence of functionals (1) that is the correspondent in function space (2) of Weyl's projective curvature tensor in n dimensions (3). Since then, I have succeeded in finding a sequence of non-tensor functionals (4) with the property that each functional of the sequence remains unaltered under an arbitrary projective functional transformation (1) of the functional affine connection. It is the object of this note to outline briefly the results obtained in the above studies. A detailed presentation with proofs as well as an account of numerous results and theorems that flow out of the ideas and methods of the present note is reserved for a series of papers to be published elsewhere.