Green's functions, Biot-Savart Operators and Linking Numbers on Negatively Curved Symmetric Spaces
Differential Geometry
2020-01-08 v1
Abstract
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Savart operator gives rise to a Gauss linking integral.
Keywords
Cite
@article{arxiv.1907.10511,
title = {Green's functions, Biot-Savart Operators and Linking Numbers on Negatively Curved Symmetric Spaces},
author = {Stefan Bechtluft-Sachs and Evangelia Samiou},
journal= {arXiv preprint arXiv:1907.10511},
year = {2020}
}