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So-called transversality relations arose first in the calculus of variations and later in the theory of infinitesimal contact transformations. For the plane such relations are of arbitrary character, but in all spaces of more than two dimensions only correspondences of certain specific types can be identified with transversality relations. Similarly, systems of extremals, which are of arbitrary character for the simplest problem of the calculus of variations, are of peculiar geometric characterdoi:10.1090/s0002-9947-1928-1501438-2 fatcat:6gzavortlbhxrhad4jbjfgc6gm