FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 2, PAGES 621-625

**About connections induced on surfaces of the projective space by
the Bortolotti clothing**

S. I. Sokolovskaja

Abstract

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The present paper introduces the notion of
the Bortolotti connection in the principal fiber space
$\$\; \backslash hat\; H(S(\backslash tilde\; M\_\{n,m\}^\{n-m\}),\backslash dot\; G\_m)\; \$$, the notion of
the pseudosurface, associated with subsurface, and
the Bortolotti clothing of a pseudosurface, which generates
the described connection.
The paper singles out a special case of the clothing,
namely, the Bortolotti clothing in the proper sense.
It is demonstrated that the Bortolotti clothing in
the proper sense of the pseudosurface, associated with a
subsurface $$S _{m}, induces
the Bortolotti clothing of the subsurface $$S
_{m} itself.
The paper sets up and solves the problem of immersion of
the Bortolotti connection in an $N$-dimensional projective
space.
It is proved that the immersion is possible, if $N\; \ge \; mn(n$-m+1)+m(m-1)/2.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k01/k012/k01218h.htm.

Last modified: October 31, 2001.