Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Details Dimensionally Dependent Tensor Identities by Double Antisymmetrisation Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

2001-05-18

arxiv.org/abs/gr-qc/0105066v1

J.Math.Phys. 43 (2002) 659-677

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 2 figures

Scientific paper

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.

Affiliated with

Also associated with

No associations

Rating

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dimensionally Dependent Tensor Identities by Double Antisymmetrisation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimensionally Dependent Tensor Identities by Double Antisymmetrisation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197236