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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...

Remark on bilinear operations on tensor fields

Jan Slovák (2020)

Archivum Mathematicum

This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Constantin Călin, Mircea Crasmareanu (2014)

Czechoslovak Mathematical Journal

We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...

Some natural operators on vector fields

Jiří M. Tomáš (1995)

Archivum Mathematicum

We determine all natural operators transforming vector fields on a manifold M to vector fields on T * T 1 2 M , dim M ≥ 2 , and all natural operators transforming vector fields on M to functions on T * T T 1 2 M , dim M ≥ 3 . We describe some relations between these two kinds of natural operators.

Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd (2001)

Commentationes Mathematicae Universitatis Carolinae

Polynomials on ℝ n with values in an irreducible Spin n -module form a natural representation space for the group Spin n . These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on ℝ n with values in these modules.

Currently displaying 121 – 140 of 178