1 citations · 3 across the 15 of their papers we have counts for
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Geometry of Projective Planes over Two-Dimensional Algebras
Maks A. Akivis, Vladislav V. Goldberg
The authors study smooth lines on projective planes over the algebra C of complex numbers, the algebra C^1 of double numbers, and the algebra C^0 of dual numbers. In the space RP^5…
Goursat's (n+1)-Webs
Vladislav V. Goldberg
We consider the Goursat's (n+1)-webs of codimension one of two kinds on an n-dimensional manifold. They are characterized by the specific closed form equations or by two special re…
Multidimensional (n+1)-Webs with Reduct Reducible Subwebs
Vladislav V. Goldberg
We find three characterizations for a multidimensional (n+1)-web W possessing a reduct reducible subweb: its closed form equations, the integrability of an invariant distribution a…
A Classification and Examples of Four-Dimensional Isoclinic Three-Webs
Vladislav V. Goldberg
A classification and examples of four-dimensional isoclinic three-webs of codimension two are given. The examples considered prove the existence theorem for many classes of webs fo…
An affine analogue of the Hartman-Nirenberg cylinder theorem
Maks A. Akivis, Vladislav V. Goldberg
Let X be a smooth, complete, connected submanifold of dimension n < N in a complex affine space A^N (C), and r is the rank of its Gauss map γ, γ(x) = T_x (X). The authors prove tha…
On the Structure of Submanifolds with Degenerate Gauss Mappings
Maks A. Akivis, Vladislav V. Goldberg
An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The auth…