Related papers: On some relativistic singular surfaces
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally…
We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in $\mathbb{C}^2$. We recall some classical obstructions and prove some deeper ones related to symplectic…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to…
This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of the normal ruled surface and focal surfaces of the initial…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real…
We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an…
We present herewith certain thoughts on the important subject of nowadays physics, pertaining to the so-called ``singularities'', that emanated from looking at the theme in terms of ADG (: abstract differential geometry). Thus, according to…
The paper collects different approaches and viewpoints on bilinear forms and hermitian forms around isolated hypersurface singularities. It gives the relations between them in precise formulas. It does not contain new results.
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
We give a bound on the number of isolated, essential singularities of determinantal quartic surfaces in 3-space. We also provide examples of different configurations of real singularities on quartic surfaces with a definite Hermitian…
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for a continuous mathematical description of fundamental physics is a natural outcome of discrete fields with discrete interactions.…