A general comparison theorem with applications to volume estimates for submanifolds
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.
In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.
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 .