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A generalization of the exterior product of differential forms combining Hom-valued forms

Christian Gross (1997)

Commentationes Mathematicae Universitatis Carolinae

This article deals with vector valued differential forms on C -manifolds. As a generalization of the exterior product, we introduce an operator that combines Hom ( s ( W ) , Z ) -valued forms with Hom ( s ( V ) , W ) -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.

A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems

Eduardo Aranda-Bricaire, Ülle Kotta (2004)


The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.

Affine connections on almost para-cosymplectic manifolds

Adara M. Blaga (2011)

Czechoslovak Mathematical Journal

Identities for the curvature tensor of the Levi-Cività connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established.

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