Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group

Details Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group

2004-04-19

arxiv.org/abs/math/0404337v1

Mathematics

Differential Geometry

18 pages

Scientific paper

This paper focuses on the development of harmonic and Clifford analysis techniques in the context of some conformally flat manifolds that arise from factoring out a simply-connected domain from $R^n$ by special arithmetic subgroups of the conformal group. Our discussion encompasses in particular the Hopf manifold $S^1 \times S^{n-1}$, conformally flat cylinders and tori and some conformally flat manifolds of genus $g \ge 2$, such as $k$-handled tori and polycylinders. This paper provides a continuation as well as an extension of our previous two papers \cite{KraRyan1,KraRyan2}. In particular, we introduce a Cauchy integral formula for hypermonogenic functions on cylinders, tori and on half of the Hopf manifold. These are solutions to the Dirac-Hodge equation with respect to the hyperbolic metric. We further develop generalizations of the Mittag-Leffler theorem and the Laurent expansion theorem for cylindrical and toroidal monogenic functions. The study of Hardy space decompositions on the Hopf manifold is also continued. Kerzman-Stein operators are introduced. Explicit formulas for the Szeg\"o kernel, the Bergman kernel and the Poisson kernel of half the Hopf manifold are given.

Affiliated with

Also associated with

No associations

Rating

Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in $R^n$ arising from Special Arithmetic Groups of the Vahlen Group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-382559