Some questions on the theory of nonholonomic complexes

V. I. Bliznikas

Itogi Nauki i Tekhniki. Seriya Problemy Geometrii. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 5 (1974), pp. 69-96

Résumé

In this paper which is a continuation of the fairly recent papers by К. J. Grincevicius and the author [2]–[3] the study of non-holonomic complex $\mathrm{NGr}(1,3,3)$ in the three-dimensional' projective space is continued. In § 1 the definition of $\mathrm{NGr}(1,3,3)$ is introduced and the algebraic structure of the first fundamental object $H^{(1)}(\mathrm{NGr}(1,3,3))$ of $\mathrm{NGr}(1,3,3)$ (in terms by G. F. Laptev [4]) is considered. In § 2 the geometrical interpretations of some comitants of the first fundamental object $H^{(1)}(\mathrm{NGr}(1,3,3))$ are given. In § 3 some invariant inner normalizations of $\mathrm{NGr}(1,3,3)$ are found and, finally, in § 4 is proved that, in general case, the first fundamental object $H^{(1)}(\mathrm{NGr}(1,3,3))$ is the principal object of non hokmomic complex $\mathrm{NGr}(1,3,3)$.