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Fundam. Prikl. Mat., 2001, Volume 7, Issue 2, Pages 621–625 (Mi fpm575)  

Short communications

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

S. I. Sokolovskaya

Sigma

Abstract: 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 $N\geq mn(n-m+1)+m(m-1)/2$.

Full text: PDF file (244 kB)

Bibliographic databases:
UDC: 514.762
Received: 01.04.2000

Citation: S. I. Sokolovskaya, “About connections induced on surfaces of the projective space by the Bortolotti clothing”, Fundam. Prikl. Mat., 7:2 (2001), 621–625

Citation in format AMSBIB
\Bibitem{Sok01}
\by S.~I.~Sokolovskaya
\paper About connections induced on surfaces of the~projective space by the~Bortolotti clothing
\jour Fundam. Prikl. Mat.
\yr 2001
\vol 7
\issue 2
\pages 621--625
\mathnet{http://mi.mathnet.ru/fpm575}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1866470}
\zmath{https://zbmath.org/?q=an:1056.53013}


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  • Фундаментальная и прикладная математика
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