nLab
vertical vector field

Context

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

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Definition

Let π:PX\pi : P \to X be a bundle in the category Diff of smooth manifolds. A vector field vΓ(P)v \in \Gamma(P) is vertical with respect to this bundle if it is in the kernel of the differential dπ:TPTXd \pi : T P \to T X.

A differential form on PP is a horizontal differential form with respect to PXP \to X it it vanishes on vertical vector fields.

  • parameterized index theorem?

Revised on September 18, 2013 22:14:07 by Urs Schreiber (145.116.129.172)