26 papers · 1 filter
On the Blaschke conjecture for 3-webs
Vladislav V. Goldberg, Valentin V. Lychagin
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linea…
Induced connections on submanifolds in spaces with fundamental groups
Maks A. Akivis, Vladislav V. Goldberg, Arto V. Chakmazyan
The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and sh…
Dually degenerate varieties and the generalization of a theorem of Griffiths--Harris
Maks A. Akivis, Vladislav V. Goldberg
The dual variety X* for a smooth n-dimensional variety X of the projective space P^N is the set of tangent hyperplanes to X. In the general case, the variety X* is a hypersurface i…
Maximum rank webs are not necessarily almost Grassmannizable
Vladislav V. Goldberg
We present an example of a 6-web W (6, 3, 2) of codimension two and of maximum rank on a six-dimensional manifold which is not almost Grassmannizable.
Linearizability of d-webs, d \geq 4, on two-dimensional manifolds
Maks A. Akivis, Vladislav V. Goldberg, Valentin V. Lychagin
We find d - 2 relative differential invariants for a d-web, d \geq 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be lin…
4-webs in the plane and their linearizability
Vladislav V. Goldberg
We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply a recently found in [AGL] the linearizability conditions for 4-webs…