Lorentzian Geometry and Related Topics

Lorentzian Geometry and Related Topics

Author: María A. Cañadas-Pinedo

Publisher: Springer

Published: 2018-03-06

Total Pages: 278

ISBN-13: 3319662902

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This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.


Global Lorentzian Geometry

Global Lorentzian Geometry

Author: John K. Beem

Publisher: Routledge

Published: 2017-09-29

Total Pages: 660

ISBN-13: 1351444700

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Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.


Introduction to Lorentz Geometry

Introduction to Lorentz Geometry

Author: Ivo Terek Couto

Publisher: CRC Press

Published: 2021-01-05

Total Pages: 351

ISBN-13: 1000223345

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Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644


Advances in Lorentzian Geometry

Advances in Lorentzian Geometry

Author: Matthias Plaue

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 154

ISBN-13: 082185352X

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Offers insight into the methods and concepts of a very active field of mathematics that has many connections with physics. It includes contributions from specialists in differential geometry and mathematical physics, collectively demonstrating the wide range of applications of Lorentzian geometry, and ranging in character from research papers to surveys to the development of new ideas.


Differential Geometry: Geometry in Mathematical Physics and Related Topics

Differential Geometry: Geometry in Mathematical Physics and Related Topics

Author: Robert Everist Greene

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 681

ISBN-13: 0821814958

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The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge


Developments in Lorentzian Geometry

Developments in Lorentzian Geometry

Author: Alma L. Albujer

Publisher: Springer Nature

Published: 2022-10-06

Total Pages: 323

ISBN-13: 3031053796

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This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Córdoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today. This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings. Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more. Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.


Recent Trends in Lorentzian Geometry

Recent Trends in Lorentzian Geometry

Author: Miguel Sánchez

Publisher: Springer Science & Business Media

Published: 2012-11-06

Total Pages: 357

ISBN-13: 1461448972

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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. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed. Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. ​ This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.


Riemannian Submersions and Related Topics

Riemannian Submersions and Related Topics

Author: Maria Falcitelli

Publisher: World Scientific

Published: 2004

Total Pages: 292

ISBN-13: 9812388966

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- First systematic exposition devoted to Riemannian submersions - Deals with current material - Contains a wide-ranging bibliography and about 350 references


Semi-Riemannian Geometry With Applications to Relativity

Semi-Riemannian Geometry With Applications to Relativity

Author: Barrett O'Neill

Publisher: Academic Press

Published: 1983-07-29

Total Pages: 483

ISBN-13: 0080570577

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This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.