Treffer: A generalization of the Schwarzian via Clifford numbers

Title:
A generalization of the Schwarzian via Clifford numbers
Authors:
Wada, Masaaki
Source:
Annales Fennici Mathematici; Vol. 23 No. 2 (1998): Volume 23, 1998; 453-460
Annales Fennici Mathematici; Vol 23 Nro 2 (1998): Volume 23, 1998; 453-460
Publisher Information:
The Finnish Mathematical Society, 1998.
Publication Year:
1998
Subject Terms:
Differentiable mappings in differential topology, Functions of hypercomplex variables and generalized variables, Projective differential geometry, Differential invariants (local theory), geometric objects
Document Type:
Fachzeitschrift Article
File Description:
application/pdf; application/xml
Language:
English
Access URL:
https://afm.journal.fi/article/view/134928
https://zbmath.org/1279104
Rights:
CC BY
Accession Number:
edsair.dedup.wf.002..5c1d281ffc63528bfc63db79b7a95b75
Database:
OpenAIRE

Weitere Informationen

A theory of the Schwarzian for sufficiently smooth local transformations of the Euclidean \(n\)-space is developped. The generalized Schwarzian given in the paper unifies the generalized Schwarzian derivatives of Ahlfors by using Clifford numbers. Various formulas relating the Schwarzian to Möbius transformations are given, and it is shown that the Schwarzian derivative vanishes for Möbius transformations. In the case of a complex analytic function, the Schwarzian derivative given in the paper is shown to coincide with the classical one.