Related papers: Anisotropic Quadratic Forms and Inversive Geometry
We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
We investigate submanifolds in space forms such that every geodesic orthogonal to the submanifold intersects a fixed totally geodesic submanifold. We obtain an application to horospheres in Hadamard manifolds.
Let $D$ be an irreducible plane curve. In this article, we first introduce a notion of a quadratic residue curve mod $D$, and study quadratic residue concis $C$ mod an irreducible quartic curve $Q$. As an application, we study a dihedral…
A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits…
In this work, we offer a historical stroll through the vast topic of binary quadratic forms. We begin with a quick review of their history and then an overview of contemporary algebraic developments on the subject.
This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the equatorial plane. The explicit form of geodesic motion is obtained in terms of incomplete elliptic integrals of…
We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $n>0$, we show that there exists a space of geodesic…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
We consider the quasihyperbolic metric, and its generalizations in both the $n$-dimensional Euclidean space $R^n$, and in Banach spaces. Historical background, applications, and our recent work on convexity properties of these metrics are…
Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical…
We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.
Nondegenerate quadratic forms over $p$-adic fields are classified by their dimension, discriminant, and Hasse invariant. This paper uses these three invariants, elementary facts about $p$-adic fields and the theory of quadratic forms to…
An axiomatic approach to the mathematical models of the isotropic cosmology.
The goal of this work is to extend Dirac-type tensor equations to a curved space. We take four 1-forms (a tetrad) as a unique structure, which determines a geometry of space-time.
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We classified…
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.