THE RICCI IDENTITY FOR GENERAL CONNECTIONS

Antonella Cabras

Key words: General connection, absolute differentiation,
Ricci identity, iterated 2-jet, difference tensor.

1991 Math. Subject Classification: 53C05, 58A20.

Abstract:
Given an arbitrary fibered manifold $Y\to M$, we introduce the second
order absolute differentiation with respect to a general connection
$\Gam$ on $Y$ and a classical linear connection $\Lam$ on $M$. Then we
generalize the Ricci identity to such a situation. The problem requires a new
geometric  operation on a subclass of the iterated 2-jets.