A generalization of Berger's rigidity theorem for positively curved manifolds
This article deals with vector valued differential forms on -manifolds. As a generalization of the exterior product, we introduce an operator that combines -valued forms with -valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
Dato un cono aperto non vuoto, convesso, regolare e affinemente omogeneo in uno spazio vettoriale reale di dimensione finita si prova che per ogni appartenente a esiste un diffeomorfismo che soddisfa le condizioni seguenti E1) ; E2) per ogni appartenente a ove è la funzione caratteristica di .
We prove that a locally symmetric and a null-complete Lorentz manifold is geodetically complete.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...