Distribution of hyperplane elements in a projective space

N. M. Ostianu

Itogi Nauki i Tekhniki. Seriya Problemy Geometrii. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 4 (1973), pp. 71-120

Résumé

In a previous paper [10] the theory of $m$-distributions in $n$-spaces was studied, the case $m=n-1$ being excluded. The purpose of this paper is to study this ease formerly omitted. The geometry of $(n-1)$-distributions in $P_n$ is constructed in an invariant analytic form. The differential neighbourhoods of first four orders are studied. Many geometric objects, subordinated to the fundamental objects are found and, as a rule, their geometric meaning is elucidated. Excluding p. 4 of § 3 no assumption about the non-vanishing of the non-holonomity tensor is made, so the results can also be applied to holonomic distributions. As an exemple the case $n=2$ is treated (§ 6).