Conformal mappings in geometric algebra (Q2883484)

The author starts with historical and private remarks on relations between algebra and geometry. As he states, his mission is to convince the world of the importance of geometric algebra as a field of differential geometry. Here, the geometric algebra \({\mathbb G}_{p,q}\) as a mathematical structure is understood as the Clifford algebra associated to the pseudo-Euclidean space \({\mathbb R}^{p,q}\) of index \((p,q)\). The author shows how this algebraic structure can be used to describe fundamental invariants of submanifolds of \({\mathbb R}^{p,q}\), such as intrinsic and extrinsic curvature. Conformal mappings of surfaces, are described in terms of algebraic operations in \({\mathbb G}_{p,q}\), so for instance Möbius transformations by Vahlen matrices.