Related papers: Generalized Ribaucour-type surfaces
Our aim is to study invariant hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, whose mean curvature is given as a linear function in the unit sphere $\mathbb{S}^n$ depending on its Gauss map. These hypersurfaces are closely…
General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our…
A surface in a Riemannian space is called of constant astigmatism if the difference between the principal radii of curvatures at each point is a constant function. In this paper we give a classification of all rotational surfaces of…
We obtain a set of generalized eigenvectors that provides a generalized spectral decomposition for a given unitary representation of a commutative, locally compact topological group. These generalized eigenvectors are functionals belonging…
A generalization of the notion of surfaces of revolution in the spaces of General Relativity is presented. We apply this definition to the case of Carter's family [A] of solutions and we study the Kerr's metric with respect the above…
We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.
A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of…
We apply the technique of jet differentials to establish a Gauss curvature estimate for an open Riemann surface $M$, equipped with a conformal metric induced from a nonconstant holomorphic map that is highly ramified over a generic…
We consider smooth Riemannian surfaces whose curvature $K$ satisfies the relation $\Delta\log|K-c|=aK+b$ away from points where $K=c$ for some $(a,b,c)\in\mathbb{R}^3$, which we call generalized Ricci surfaces. We prove some isometric…
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci…
A geometric construction is provided that associates to a given flat front in $\mathbb{H}^3$ a pair of minimal surfaces in $\mathbb{R}^3$ which are related by a Ribaucour transformation. This construction is generalized associating to a…
We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized…
This paper refers to the study of generalized Struve type function. Using generalized Galue type Struve function (GTSF) by Nisar et al. [13], we derive various integral transform, including Euler transform, Laplace transform, Whittakar…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…
In this paper, we have first given easily the characterization of special curves with the help of the Rotation minimizing frame (RMF). Also, rectifying-type curves are generalized n-dimensional space $R_{n}$.
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…