Roman Matsyuk (Institute for Applied Problems in Mechanics and Mathematics, Lviv)

Variational principle for the 2-dimensional concircular geometry

The concircular geometry deals with curves of  constant first curvature and of zero second curvature. The corresponding third-order differential equation of such a path coincides with the equation of  uniformly accelerated test particle in General Relativity. We extend to the case of general 2-dimensional  pseudo-Riemannian geometry the following result: there exists the unique Lorentz-invariant variational equation of the third order, the integral paths of which have constant curvature and include the usual straight geodesics: