20 research outputs found
Frobenius 3-Folds via Singular Flat 3-Webs
We give a geometric interpretation of weighted homogeneous solutions to the
associativity equation in terms of the web theory and construct a massive
Frobenius 3-fold germ via a singular 3-web germ satisfying the following
conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the
Chern connection form is holomorphic, 3) the curvature form vanishes
identically
Gronwall's conjecture for 3-webs with infinitesimal symmetries
We study non-flat planar 3-webs with infinitesimal symmetries. Using
multi-dimensional Schwarzian derivative we give a criterion for linearization
of such webs and present a projective classification thereof. Using this
classification we show that the Gronwall conjecture is true for 3-webs
admitting infinitesimal symmetries.Comment: 20 page
Hexagonal circular 3-webs with polar curves of degree three
The paper reports the progress with the classical problem, posed by Blaschke
and Bol in 1938. We present new examples and new classifications of natural
classes of hexagonal circular 3-webs. The main results is the classification of
hexagonal circular 3-webs with polar curves of degree 3.Comment: 39 pages, 9 figure