×

On connections, determined by a normal cubic on a smooth surface. (English) Zbl 0862.53009

Shelekhov, A. M. (ed.), Webs and quasigroups. Tver: Tver State University. 97-105 (1992).
Let \(V^2\) be a smooth surface in a projective space \(P^3\) and \(N\) be a normal cubic curve in \(P^3\). If we illuminate \(V^2\) from the points of \(N\), then the shadow-lines on \(V^2\) form the so-called coordinate web. On the other hand, the curve \(N\) determines some invariant affine connections on \(V^2\). The invariants of the coordinate 3-web are interpreted in terms of these connections.
For the entire collection see [Zbl 0748.00014].

MSC:

53A20 Projective differential geometry
20N05 Loops, quasigroups
53A60 Differential geometry of webs
53B05 Linear and affine connections
PDFBibTeX XMLCite