On the structure of some irrotational vector fields.
Si considerano due spazi e , Riemanniani e a metrica eventualmente indefinita, riferiti a sistemi di co-ordinate e ; e inoltre un doppio tensore associato ai punti e . Si pensa dato da una funzione di altri tali doppi tensori e di variabili puntuali , e ; poi si considera la funzione composta Nella Parte I si scrivono due regole per eseguire la derivazione totale di questa, connessa con una mappa
Extending the construction of the algebra of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M, via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its members are smooth functions depending-via a third slot-on so-called transport operators, in addition to slots...
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.