FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 2, PAGES 621-625
S. I. Sokolovskaja
Abstract
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The present paper introduces the notion of the Bortolotti
connection in the principal fiber space
$\hat H(S(\tilde M_{n,m}^{n-m}),\dot G_m)$ ,
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 $\Sigma_m$ ,
induces the Bortolotti clothing of the subsurface $\Sigma_m$ 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
$N\geq mn(n-m+1)+m(m-1)/2$ .
All articles are published in Russian.
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Last modified: October 31, 2001.