Dimensionally dependent tensor identities by double antisymmetrization
2002 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 43, no 1, 659-677 p.Article in journal (Refereed) Published
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 greater than or equal ton. We generalize 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 antisymmetrizing 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. (C) 2002 American Institute of Physics.
Place, publisher, year, edition, pages
2002. Vol. 43, no 1, 659-677 p.
IdentifiersURN: urn:nbn:se:liu:diva-49040OAI: oai:DiVA.org:liu-49040DiVA: diva2:269936