Related papers: The Classification of Surfaces
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that…
Surface topography refers to the geometric micro-structure of a surface and defines its tactile characteristics (typically in the sub-millimeter range). High-resolution 3D scanning techniques developed recently enable the 3D reconstruction…
We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…
This dissertation contains a comprehensive study of the topology of 2-manifolds and a complementary analysis of the work done by Edwin E. Moise, L. V. Ahlfors and Ian Richards. Our aim is to study the well known classification of surfaces.…
We give a complete description and classification of locally homogeneous real hypersurfaces in $\mathbb C^3$. Various groups of mathematicians have been studying this problem in the last 25 years, and several significant classes of…
An expository description of smooth cubic curves in the real or complex projective plane.
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
The simplest version of the Spin-polynomial invariants of the underlying differentiable structures of algebraic surfaces were considered and the simplest arguments were used in order to distinguish the underlying smooth structures of…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
Simple properties of the Gauss map characterise important classes of surfaces in $\Rq$: $R$-surfaces, the real version of plane complex curves; Lagrangean surfaces; isoclinic surfaces.
We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to…
In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the…
The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…
In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…
We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.