Non-Euclidean geometry

The volume consists of a set of surveys on geometry in the broad sense.

This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature.

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common?

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein's spacetime in one accessible, self-contained volume.

College geometry students, professors interested in undergraduate research and secondary geometry teachers will find three rich environments in this textbook.

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms.

Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques.

The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism.

The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism.

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

An important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view.

Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

A Fields medalist recounts his lifelong effort to uncover the geometric shape-the Calabi-Yau manifold-that may store the hidden dimensions of our universe.

Hyperbolic Dynamics and Brownian Motion illustrates the interplay between distinct domains of mathematics.

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose.

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose.

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein's spacetime in one accessible, self-contained volume.

This undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers.