Strong Hamel functions and symmetries

Abstract

For the geodesic spray of a Finsler space, a strong Hamel function is a Hamel function that is the geodesic derivative of a $0$-homogeneous potential function. Similarly, strong dual symmetries and strong dynamical symmetries are geodesically invariant $1$-forms and vector fields, respectively, associated with $0$-homogeneous potential functions. We prove that strong Hamel functions can be characterized in terms of strong dual symmetries and strong dynamical symmetries. We show that projective deformations by strong Hamel functions preserve the $\ddot{I}‡$-curvature and analyse the relationship with other classes of functions (Funk and weak Funk functions) that preserve the curvature tensors under projective deformations.

accepted version