Holonomy group and generalized Maslov classes of submanifolds of spaces with an affine connection (Q1814467)

A generalization of the Maslov characteristic classes and indices [the author, Sov. Math., Dokl. 39, No. 1, 214-217 (1989); translation from Dokl. Akad. Nauk SSSR 304, No. 6, 1302-1305 (1989; Zbl 0687.58009)] is studied. Maslov classes for submanifolds in spaces with affine connection and for Lagrange submanifolds in symplectic manifolds are built. The following application to minimal surfaces is shown: the conjecture of A. T. Fomenko that generalized Maslov classes vanish is proved for the large class of minimal surfaces.