ON SOME NEW TENSORS AND THEIR PROPERTIES IN A FOUR-DIMENSIONAL FINSLER SPACE-II
Journal Title: International Journal of Applied Mathematics & Statistical Sciences - Year 2019, Vol 8, Issue 4
Abstract
Certain new tensors have been defined and studied in a Finsler space by Rastogi[4], while recently Rastogi[6] has introduced some new tensors Dijk and Qijketc. in a Finsler space of three dimensions in the following form: Dijk = D(1)mimjmk + D(2)ninjnk + Σ(ijk){D(3) mimjnk-D(1) minjnk} (1.1) and Qijk = {D(1) / 0 -3 D(3) h0} mimjmk + (D(2) / 0 -3D(1)h0) ninjnk + Σ(ijk)[{(D (3) / 0 +3 D(1)h0} mimjnk - {D(1)/ 0+ (D(2)- 2 D(3)) h0} minjnk] (1.2) The tensor Dijk so introduced satisfies Dijk li = 0 and Dijkgjk = Di = D ni and is similar to Cijk while Qijk = Dijk/ 0is similar to Pijk. The purpose of the present paper is to introduce tensors 1Dijk and 2Dijkin a Finsler spaceof four dimensions F4 and study some of their properties. It is important to notice that in F4 instead of one Dijk,we have two such tensors.
Authors and Affiliations
Rastogi S. C.
Keywords
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