2008/02/06 by Roman Ya. Matsyuk, Roman Matsyuk · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Elasticity and Wave Propagation #Geotechnical and Geomechanical Engineering #Material Science and Thermodynamics #math-ph #math.DG #math.MP #msc:49N45 #msc:53A40 #msc:70H50 #msc:83C10
paper · pdf · doi:10.3842/sigma.2008.016
published as SIGMA 4 (2008), 016, 11 pages · This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ Corrections: Signs in formulae 3.17, 3.18, 3.21, 3.22, next to A.14
openalex publication_date 2008/02/06 · arxiv created 2008/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.