1997/03/17 by Norbert Straumann, Straumann, Norbert
Computer Science · Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Astrophysics (astro-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #astro-ph #gr-qc
paper · pdf · doi:10.48550/arxiv.astro-ph/9703103
12 pages, REVTeX, two postscript figures included
arxiv created 1997/03/17 · openalex publication_date 1997/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The elegance and usefulness of a complex formulation of the basic lensing equations is demonstrated with a number of applications. Using standard tools of complex function theory, we present, for instance, a new proof of the fact that the number of images produced by a regular lens is always odd, provided that the source is not located on a caustic. Several differential and integral relations between the mean curvature and the (reduced) shear are also derived. These emerge almost automatically from complex differentiations of the differential of the lens map, together with Stokes' theorem for complex valued 1-forms.