About representation of two-dimensional clothing sites in tangent and normal stratifications of multi-dimensional surface of Euclede space

In the n-dimensional Euclede space En with the current point A the m-surface S/sub m/ = (A)/sub m/ with the tangent m-n planes L/sub m/ and normal planes P /spl perp/ L/sub m/ in the corresponding points A /spl isin/ S/sub m/ is considered. Then, the tangent (S/sub m/;L/sub m/) and normal (S/sub m/;P) stratifications are invariantly associated with the m-surface S/sub m/ /spl sub/ E/sub n/. In the corresponding clothings in these stratifications two-dimensional planes L/sub 2//sup 1/ /spl sub/ L/sub m/ and P/sub 2/ /spl sub/ P/sub 1/, which pass through the point A /spl isin/ S/sub m/, are given. The symbol /spl chi/ /spl isin/ L/sub 2//sup 1/ denotes the straight line in L/sub 2//sup 1/ passing through A which is called direction. The symbol T/sub z/(/spl chi/) denotes a tangent linear subspace of the 1-family of straight lines z /spl isin/ L/sub m/ passing through A towards /spl chi/, that is to say, to the 1-family formed by the straight lines Z along the direction /spl chi/.