Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 18 (2008), No. 1, 093--123
Copyright Heldermann Verlag 2008

Transvection and Differential Invariants of Parametrized Curves

Gloria Marí Beffa
Mathematics Department, University of Wisconsin, Madison, WI 53706, U.S.A.

Jan A. Sanders
Mathematics Department, Vrije Universiteit, 1081 HV Amsterdam, Netherlands

We describe an sl2 representation in the space of differential invariants of parametrized curves in homogeneous spaces. The representation is described by three operators, one of them being the total derivative D. We use this representation to find a basis for the space of differential invariants of curves in a complement of the image of D, and so generated by transvection. These are natural representatives of first cohomology classes in the invariant bicomplex. We describe algorithms to find these basis and study most well-known geometries.

Keywords: Transvectant, differential invariants, curves, affine manifold, symmetric manifold.

MSC: 13A50, 53A55

[ Fulltext-pdf  (288  KB)] for subscribers only.