Kinematics of vector fields

Abstract

Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with the covariant and with the Lie-differential operator. Classification of the linear transports on the basis of the connections between the connections is given. Notion of relative velocity and relative acceleration for vector fields are determined. By means of these kinematic characteristics several other types of notions as shear velocity, shear acceleration, rotation velocity, rotation acceleration, expansion velocity and expansion acceleration are introduced and on their basis auto-parallel and non-isotropic (non-null) vector fields are classified.

44 pages, LaTeX 2e, Published in Complex structures and vector fields. (World Scientific, Singapore 1995), pp. 61-113

Cited by in corpus (8)

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• Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces
• Mechanics of Continuous Media in $({\bar{L}}_n,g)$-Spaces. II. Relative velocity and deformations
• Mechanics of Continuous Media in $({\bar{L}}_n,g)$-spaces. I. Introduction and mathematical tools
• Null vector fields in spaces with affine connections and metrics. Doppler's effect, Hubble's effect, and aberration's effect
• Centrifugal (centripetal) and Coriolis velocities and accelerations in spaces with affine connections and metrics as models of space-time
• Relative velocity and relative acceleration induced by the torsion in (pseudo) Riemannian spaces with torsion and in spaces with an affine connection and metrics
• Weyl's spaces with shear-free and expansion-free conformal Killing vectors and the motion of a free spinless test particle