FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 65-79

**$4$-webs on hypersurfaces of
$4$-axial space**

V. V. Zabrodin

Abstract

View as HTML
View as gif image

V. B. Lazareva investigated $3$-webs formed by shadow
lines on a surface embedded in $3$-dimensional projective
space is assuming that the lighting sources are situated on
$3$ straight
lines.
The results were used, in particular, for the solution of Blaschke
problem of classification of regular $3$-webs formed by pencils of
circles in a plane.
In the present paper, we consider a $4$-web $W$ formed by shadow surfaces
on a hypersurface $V$ embedded in $4$-dimensional projective
space assuming that the lighting sources are situated on $4$ straight lines.
We call the projective $4$-space with $4$ fixed straight lines
a $4$-axial
space.
Structure equations of $4$-axial space and of the
surface $V$,
asymptotic tensor of $V$, torsions and curvatures
of $4$-web $W$, and connection form of
invariant affine connection associated with $4$-web $W$ are found.

Location: http://mech.math.msu.su/~fpm/eng/k10/k101/k10106h.htm

Last modified: March 11, 2011