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A tutorial on conformal groups

Ian Porteous — 1996

Banach Center Publications

Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to p , q , the real vector space p + q , furnished with the quadratic form x ( 2 ) = x · x = - x 1 2 - x 2 2 - . . . - x p 2 + x p + 1 2 + . . . + x p + q 2 , and especially with a description of this group that involves Clifford algebras.

Some remarks on duality in S 3

Ian Porteous — 1999

Banach Center Publications

In this paper we review some of the concepts and results of V. I. Arnol’d [1] for curves in S 2 and extend them to curves and surfaces in S 3 .

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