Related papers: Hyperbolic geometry
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…
An introduction to Hyperbolic Analysis is presented.
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
This book is a regular textbook of analytical geometry covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The stress is made on vector algebra by using skew-angular…
The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
This is an introductory text to differential geometry (written in Polish) aimed for high-school students.
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry of Lorentz, Einstein and Minkowski comes from a projective…
We define and study hyperbolic extensions.
Consider the Poincare disc model for hyperbolic geometry. In this paper, a convenient computational formula is developed along with an aesthetic geometric interpretation. Two proofs, one geometric and one analytical, of each result are…
We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…
Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hyperbolic space has recently gained rapid traction for learning…