9 papers · 1 filter
On conformal invariance of isotropic geodesics
Maks A. Akivis, Vladislav V. Goldberg
We consider real isotropic geodesics on manifolds endowed with a pseudoconformal structure and their applications to the theory of lightlike hypersurfaces on such manifolds, the ge…
The Darboux mapping of canal hypersurfaces
Maks A. Akivis, Vladislav V. Goldberg
The geometry of canal hypersurfaces of an n-dimensional conformal space C^n is studied. Such hypersurfaces are envelopes of r-parameter families of hyperspheres, 1 \leq r \leq n-2.…
The geometry of lightlike hypersurfaces of the de Sitter space
Maks A. Akivis, Vladislav V. Goldberg
It is proved that the geometry of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 is directly connected with the geometry of hypersurfaces of the conformal space C^n. This…
On a normalization of a Grassmann manifold
Maks A. Akivis, Vladislav V. Goldberg
On the Grassmann manifold G (m, n) of m-dimensional subspaces of an n-dimensional projective space P^n, a certain supplementary construction called the normalization is considered.…
Singular points of lightlike hypersurfaces of the de Sitter space
Maks A. Akivis, Vladislav V. Goldberg
The authors study singular points of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 and the geometry of hypersurfaces and use them for construction of an invariant normal…
A conformal differential invariant and the conformal rigidity of hypersurfaces
Maks A. Akivis, Vladislav V. Goldberg
For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by…