Related papers: Geometry on real projective Cayley-Klein spaces
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…
We explore offsets of Cayley ovals, by networking with different kinds of software. Using their specific abilities, algebraic, geometric, dynamic, we conjecture interesting properties of the offsets. For a given progenitor (the given plane…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
Given an embedding of a projective variety into projective space, we study the structure of the space of all linear projections that, when composed with the embedding, give a Galois morphism from the variety to a projective space of the…
We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the…
In this work we discuss the notion of stationary curves of the length functional, the so-called (weak) geodesics, on a Riemannian manifold. The motivation behind this work is to give a detailed description of many key concepts from…
We define two generalizations of the totally nonnegative Grassmannian and determine their topology in the case of real projective space. We find the spaces to be PL manifolds with boundary which are homotopy equivalent to another real…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of…
The paper contributes to the important and urgent problem to extend the physical theory of space-time in a Finsler-type way under the assumption that the isotropy of space is violated by a single geometrically distinguished spatial…
We analyse the geometric properties of the high derivatives of the distance function from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its covariant derivatives of…
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
The Siegel-Jacobi space is a non-symmetric homogeneous space which is very important geometrically and arithmetically. In this short paper, we propose the basic problems in the geometry of the Siegel-Jacobi space.
Here, a non-linear analysis method is applied rather than classical one to study projective Finsler geometry. More intuitively, by means of an inequality on Ricci-Finsler curvature, a projectively invariant pseudo-distance is introduced and…
We review Bacry and Levy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous…
The geodesic distance between points in real hyperbolic space is a hypermetric, and hence is a kernel negative type. The proof given here uses an integral formula for geodesic distance, in terms of a measure on the space of hyperplanes. An…
The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…