ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 53, 58 Ramirez de Arellano, Enrique, Research and Advanced Studies Centre (CINVESTAV), Mexico City, Mexico Almost-Clifford structures on manifolds Almost-Clifford structures can be introduced on differentiable manifolds in a similar way as almost-complex structures and almost-quaternionic structures. Namely, J^{1}, …, J^{n} are fiberwise endomorphisms of the tangent bundle T (X) of the n-dimensional manifold X such that J^{r}J^{s} + J^{s}J^{r} = −2δ(r, s)I, (r, s + 1, …, n), where I is the identity endomorphism on T (X). Almost-Clifford manifolds are necessarily of dimension (2^{n})k, with k a natural number. The differential of a Clifford analytic mapping between almost-Clifford manifolds (i. e. whose differential is compatible with the almost-Clifford structures) is a Clifford linear mapping of the corresponding tangent spaces. This concept is a simple and natural one and for n = 1 coincides with holomorphy in one complex variable, for n = 2 with Q-holomorphy in quaternionic analysis (which is different from Fueter-regularity), but it is different from the nongenic concept as given f. i. in Brackx, Delanghe, Sommen and Soucek. Reference: W. Krolikowski, On Fueter-Hurwitz regular mappings, Dissertationes Math. 353 (1996)