Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-04-26
Rept.Math.Phys.60:39-53,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages LaTeX file, Changed title, Changed content, Added references, Physical features stressed
Scientific paper
10.1016/S0034-4877(07)00020-1
In this paper we discuss curvature tensors in the context of Absolute Parallelism geometry. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection. Using the Bianchi identities some other identities are derived from the expressions obtained. These identities, in turn, are used to reveal some of the properties satisfied by an intriguing fourth order tensor which we refer to as Wanas tensor. A further condition on the canonical connection is imposed, assuming it is semi-symmetric. The formulae thus obtained, together with other formulae (Ricci tensors and scalar curvatures of the different connections admitted by the space) are calculated under this additional assumption. Considering a specific form of the semi-symmetric connection causes all nonvanishing curvature tensors to coincide, up to a constant, with the Wanas tensor. Physical aspects of some of the geometric objects considered are mentioned.
Sid-Ahmed Amr M.
Youssef Nabil L.
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