Related papers: On Real Projective Plane Constructions and Their I…
This paper is a continuation of the paper [5] dealing with dynamics of dianalytic transformations of nonorientable Klein surfaces. We are examining mainly the transformations of the real projective plane $P^{2}, $ whose orientable double…
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the…
In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not…
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
We investigate the effect of a mirror-symmetry plane in multiple-scattering media under plane-wave illumination along the symmetry plane. Designed and fabricated samples' optical transport properties are compared quantitatively with…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and…
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high…
This is a revised version of a part of the author's preprint "On p-adic uniformization of fake projective planes" (preprint, Max-Planck-Institut fuer Mathematik, 1998 (121)). In this paper we construct explicitly a Shimura surface of…
Each elliptic curve can be embedded uniquely in the projective plane, up to projective equivalence. The hessian curve of the embedding is generically a new elliptic curve, whose isomorphism type depends only on that of the initial elliptic…
New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in…
In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves…
We study the GIT-quotient of the Cartesian power of projective space modulo the projective orthogonal group. A classical isomorphism of this group with the Inversive group of birational transformations of the projective space of one…
We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in…
We develop an inversive geometry for anisotropic quadradic spaces, in analogy with the classical inversive geometry of a Euclidean plane.
We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection…
We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…
Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…
We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain…
Projection mapping seamlessly merges real and virtual worlds. Although much effort was made to improve its image qualities so far, projection mapping is still unnatural. We introduce the first steps towards natural projection mapping by…