Spaces with torsion from embedding and the special role of autoparallel trajectories
arXiv:gr-qc/9709067 · doi:10.1016/S0370-2693(98)00421-3
Abstract
As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically speaking, we define the tangent (velocity) space of the embedded space imposing non-holonomic constraints upon the tangent space of the embedding space. Parallel transport in the embedded space is determined as an induced parallel transport on the surface of constraints. Gauss' principle of least constraint is used to show that autoparallels realize a constrained motion that has a minimal deviation from the free, unconstrained motion, this being a mathematical expression of the principle of inertia.
LaTeX file in src, no figures. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re259/preprint.html
Cited by in corpus (10)
- Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor
- Constraining spacetime torsion with the Moon and Mercury
- The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond
- Elie Cartan's torsion in geometry and in field theory, an essay
- Constraining spacetime torsion with LAGEOS
- Universality Principle for Orbital Angular Momentum and Spin in Gravity with Torsion
- Constrained Systems and Analytical Mechanics in Spases with Torsion
- Gravitomagnetic effect and spin-torsion coupling
- Spinless Matter in Transposed-Equi-Affine Theory of Gravity
- Principal Autoparallel Analysis: Data Analysis in Weitzenböck Space