A study on the tensor sup(*)gsup(ij) in Xn

The tensor sup(*)gsup(ij) is very useful, particularly for the study of the unified field theory. Especially, the representation of sup(*)gsup(ij) in terms of gsub(ij) is a matter of interest for various applications. The purpose of the present paper is to obtain the generalized representation of sup(*)gsup(ij) in terms of gsub(ij) in a generalized n-dimentional Riemannian space Xn, using the concept of n-dimentional indicators. The results obtained in the present paper will contribute the development of the n-dimentional sup(*)g-UFT. (author)