Related papers: Circular tractrices and generalized Dini surfaces
We study the congruence of bitangent lines of an irreducible surface in the 3-dimensional projective space in arbitrary characteristic, with special attention to quartic surfaces with rational double points and, in particular, Kummer…
We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…
We classify rotational surfaces in a normed 3-space with rotationally symmetric norm whose principal curvatures satisfy a linear relation.
In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.
We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.
We classify the minimal surfaces of general type with $K^2 \leq 4\chi-8$ whose canonical map is composed with a pencil, up to a finite number of families. More precisely we prove that there is exactly one irreducible family for each value…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
We consider algebraic surfaces, recently constructed by Schreieder, that are smooth models of the quotient of the self-product of a complex hyperelliptic curve by a $(\mathbb{Z}/3^c\mathbb{Z})$-action. We show that these surfaces are…
We classify compact complex surfaces which contain a Zariski open subset whose universal covering is the cylinder DxC.
Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.
In this study, we define a family of ruled surfaces in the Euclidean 3-space E^3 and called similar ruled surfaces. We obtain some properties of these special surfaces and we show that developable ruled surfaces form a family of similar…
In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation…
We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…
In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere by so called rectangular diagrams. The formalism proved useful for comparing Legendrian knots. The aim of this paper is to…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
The aim of this note is to point out an interesting fact related to the elliptic genus of complex algebraic surfaces in the context of Mathieu moonshine. We also discuss the case of 4-folds.
The higher order contact of a quadric with a surface in $3$-space at a non-degenerate point is obtained by the Moutard quadric in the Darboux direction. In this paper, we discuss the extension of this result to hypersurfaces in arbitrary…
We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are…