O bodové deformaci kongruencí rovin v pětirozměrném projektivním prostoru
O projektivních deformacích kongruencí rovin v -rozměrném projektivním prostoru
On a new normalization for tractor covariant derivatives
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
On a result of Tzitzeica and a new asymptotic transformation of minimal projective surfaces
On curvature collineations on simple conformally recurrent manifolds
On inversions of van der Grinten projections
Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I--IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement...
On singular projective deformations of two second class totally focal pseudocongruences of planes.
On some classes of curves in a projective space
On special plane nets
On surfaces and their contours.
On the Converse of Weyl's Conformal and Projective Theorems
On the integral geometry of the linear subspaces in a biplanar space
On the local differential geometry of complete intersections
Polarités définies par un triangle
Une polarité d’un plan projectif est une application, souvent involutive, envoyant un point générique sur une droite générique et réciproquement. La polarité la plus classique est la polarité par rapport à une conique, mais d’autres existent : la polarité harmonique par rapport à un triangle, les polarités par rapport à une courbe algébrique de degré supérieur, la polarité par rapport à un convexe.Dans cet article nous introduisons une notion de polarité par rapport à un triangle du plan projectif,...
Position vectors of curves in the galilean space G
Projective Homogeneity.
Projective relatedness and conformal flatness
This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening...
Projective spaces of second order.
Grassmannians of higher order appeared for the first time in a paper of A. Szybiak in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian, the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group.
Projektivní deformace přímkových kongruencí vnořených do šestirozměrných projektivních prostorů