On the conformal areal spaces of the submetric class II. The Deductions of some Identities

✍ Scribed by Om P. Singh

• Publisher: John Wiley and Sons
• Year: 1973
• Tongue: English
• Weight: 300 KB
• Volume: 58
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19730580110

✦ Synopsis

The present paper is in the continuity of the author's previous paper [l] 1). In this paper, we shall show certain properties of the curvature tensors of a conformal areal spare of the submetric class and deduce some identities. The notations used in the present paper are the same as those employed in [I] and by previous authors [z7 3, 4, 51 without explanations.

Let A!:) and 2::) be two distinct n-ctimonsionsl areal spaces of the submetric class of which the fundamental functions are given by F (xi, p i ) 2) and P (xi7 p i ) respectively with the same system of coordinates. These two spaces Aim) and A?) are called conformally related, if their respective four index metric tensors g$ and @ are related by 1) Numbers in brackets refer t o the references a t the end of the paper.

2. Latin indices h, i, j, k , . . . run from 1 to 12 and Greek indices a, B, y. 8, . . . from 1 t o