Questions relating to the search of geodesics in a series of left-invariant problems with sub-Lorentzian or Finsler structure are under consideration. Explicit formulae for extremals are found in terms of trigonometric functions of convex trigonometry. In sub-Lorentzian problems the machinery of the new trigonometric functions _ and _, generalizing and to the case of an unbounded convex set R², is particularly useful. Bibliography: 18 titles.
Ladeishchikov et al. (Wed,) studied this question.