4 papers · 2 filters
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…
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…
Equivalence of Examples of Sacksteder and Bourgain
Maks A. Akivis, Vladislav V. Goldberg
Finding examples of tangentially degenerate submanifolds (submanifolds with degenerate Gauss mappings) in an Euclidean space that are noncylindrical and without singularities…