Abstract
In this paper we use a calculus of differential forms which is defined using an axiomatic approach. We then define integration of differential forms over chains in a new way and we present a short proof of Stokes’ formula using distributional techniques. We also consider differential forms in Clifford analysis, vector differentials and their powers. This framework enables an easy proof for a Cauchy formula on a k-surface. Finally, we discuss how to compute winding numbers in terms of the monogenic Cauchy kernel and the vector differentials with a new approach which does not involve cohomology of differential forms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Sabadini, I., Sommen, F. (2016). Differential Forms and Clifford Analysis. In: Bernstein, S., Kähler, U., Sabadini, I., Sommen, F. (eds) Modern Trends in Hypercomplex Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42529-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-42529-0_14
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-42528-3
Online ISBN: 978-3-319-42529-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)