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Particular trace decompositions and applications of trace decomposition to almost projective invariants

Mircea Crâşmăreanu (2001)

Mathematica Bohemica

First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.

Principal prolongations and geometries modeled on homogeneous spaces.

Slovák, J. (1996)

Archivum Mathematicum

Principal prolongations and geometries modeled on homogeneous spaces

Jan Slovák (1996)

Archivum Mathematicum

We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.

Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds

Gloria Marí Beffa (2008)

Annales de l’institut Fourier

In this paper we describe moving frames and differential invariants for curves in two different $| 1 |$ -graded parabolic manifolds $G / H$ , $G = O (p + 1, q + 1)$ and $G = O (2 m, 2 m)$ , and we define differential invariants of projective-type. We then show that, in the first case, there are geometric flows in $G / H$ inducing equations of KdV-type in the projective-type differential invariants when proper initial conditions are chosen. We also show that geometric Poisson brackets in the space of differential invariants of curves in $G / H$ can be reduced...

Displaying 1 – 4 of 4

Particular trace decompositions and applications of trace decomposition to almost projective invariants

Principal prolongations and geometries modeled on homogeneous spaces.

Principal prolongations and geometries modeled on homogeneous spaces

Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds

Currently displaying 1 – 4 of 4