Conformal derivative and conformal transports over spaces with contravariant and covariant affine connections and metrics

Details Conformal derivative and conformal transports over spaces with contravariant and covariant affine connections and metrics Conformal derivative and conformal transports over spaces with contravariant and covariant affine connections and metrics

2000-11-03

arxiv.org/abs/gr-qc/0011007v1

Int.J.Mod.Phys. A15 (2000) 679-695

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, LaTeX

Scientific paper

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as ''conformal'' transports and investigated over spaces with contravariant and covariant affine connections (whose components differ not only by sign) and metrics. They are more general than the Fermi-Walker transports. In an analogous way as in the case of Fermi-Walker transports a conformal covariant differential operator and its conformal derivative are defined and considered over the above mentioned spaces. Different special types of conformal transports are determined inducing also Fermi-Walker transports for orthogonal vector fields as special cases. Conditions under which the length of a non-null contravariant vector field could swing as a homogeneous harmonic oscillator are established. The results obtained regardless of any concrete field (gravitational) theory could have direct applications in such types of theories. PACS numbers: 04.90.+e; 04.50.+h; 12.10.Gq; 02.40.Vh

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