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.

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Last modified: October 31, 2001.