相关论文: On Circular Tractrices in $\mathbb R^3$
In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.
Classical and wave properties of microlasers with the shape of a truncated pseudosphere are investigated through experiments and numerical simulations. These pseudosphere microlasers are surface-like organic microlasers with constant…
In the present paper, loxodromes, which cut all meridians and parallels of twisted surfaces (that can be considered as a generalization of rotational surfaces) at a constant angle, have been studied in Euclidean 3-space and some examples…
We study the distribution of algebraic points on K3 surfaces.
A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as…
In Euclidean geometry, the Pythagorean theorem is presented as an equation involving three squares. This paper explores how analogous expressions may be identified in spherical and hyperbolic geometries.
We describe decomposition formulas for rotations of $R^3$ and $R^4$ that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
In this article, spherical indicatrices of a curve and helices are re-examined using both the algebraic structure and the geometric structure of non-Newtonian (multiplicative) Euclidean space. Indicatrices of a multiplicative curve on the…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…
Inscribed angles are investigated in taxicab geometry with application to the existence and uniqueness of inscribed and circumscribed taxicab circles of triangles.
We apply the loop group method developed by Zakharov-Shabat, Terng-Uhlenbeck and Toda to the study of symmetries of pseudospherical surfaces in R^3. In this paper (part I) we consider the general theory, while in a second paper (part II) we…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
An examples of solutions of the equation for curvature of congruence of cycles are constructed. Their properties are discussed.
In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices,…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…
An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that any two of the curves are either disjoint or intersect in exactly two crossing points. We call an arrangement intersecting if…