Open AccessBoundary rigidity for Randers metrics
Author(s) -
Keijo Mönkkönen
Publication year - 2021
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.112492
Subject(s) - rigidity (electromagnetism) , boundary (topology) , norm (philosophy) , mathematics , boundary value problem , mathematical analysis , finsler manifold , pure mathematics , metric (unit) , physics , geometry , curvature , ricci curvature , philosophy , quantum mechanics , operations management , epistemology , economics
If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics where the reversible Finsler norm is induced by a Riemannian metric which is boundary rigid. Our theorems generalize Riemannian boundary rigidity results to some non-reversible Finsler manifolds. We provide an application to seismology where the seismic wave propagates in a moving medium.