A NOTE ON THE EXISTENCE OF TUBULAR NEIGHBOURHOODS ON FINSLER MANIFOLDS AND MINIMIZATION OF ORTHOGONAL GEODESICS TO A SUBMANIFOLD

摘要

In this note, we prove that given a submanifold P in a Finsler manifold (M, F), (i) the orthogonal geodesics to P minimize the distance from P at least in some interval, (ii) there exist tubular neighbourhoods around each point of P, (iii) the distance from P is smooth in some open neighbourhood of P (but not necessarily in P).