Books in Geometry

Crystal Symmetries

1st Edition
Volume 17
July 26, 2017
B. K. Vainshtein + 1 more
English
eBook
9 7 8 1 4 8 3 2 9 9 1 0 5

Crystal Symmetries is a timely account of the progress in the most diverse fields of crystallography. It presents a broad overview of the theory of symmetry and contains state of the art reports of its modern directions and applications to crystal physics and crystal properties. Geometry takes a special place in this treatise. Structural aspects of phase transitions, correlation of structure and properties, polytypism, modulated structures, and other topics are discussed. Applications of important techniques, such as X-ray crystallography, biophysical studies, EPR spectroscopy, crystal optics, and nuclear solid state physics, are represented. Contains 30 research and review papers.

Topology and Geometry for Physicists

1st Edition
January 4, 1988
Charles Nash + 1 more
English
eBook
9 7 8 0 0 8 0 5 7 0 8 5 3

Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book. An obvious omission here is general relativity--we apologize for this. We originally intended to discuss general relativity. However, both the need to keep the size of the book within the reasonable limits and the fact that accounts of the topology and geometry of relativity are already available, for example, in The Large Scale Structure of Space-Time by S. Hawking and G. Ellis, made us reluctantly decide to omit this topic.

Eigenvalues in Riemannian Geometry

2nd Edition
Volume 115
November 7, 1984
Isaac Chavel
English
Hardback
9 7 8 0 1 2 1 7 0 6 4 0 1
eBook
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The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.

Groups & Geometric Analysis

1st Edition
Volume 113
June 30, 1984
Sigurdur Helgason
English
eBook
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Semi-Riemannian Geometry With Applications to Relativity

1st Edition
Volume 103
June 28, 1983
Barrett O'Neill
English
Hardback
9 7 8 0 1 2 5 2 6 7 4 0 3
eBook
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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.

Dynamical Systems and Microphysics

1st Edition
December 2, 2012
Andre Avez
English
eBook
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Dynamical Systems and Microphysics: Geometry and Mechanics contains the proceedings of the Second International Seminar on Mathematical Theory of Dynamical Systems and Microphysics held at the International Center for Mechanical Sciences in Udine, Italy on September 1-11, 1981. Contributors explore the geometry and mechanics of dynamical systems and microphysics and cover topics ranging from Lagrangian submanifolds and optimal control theory to Hamiltonian mechanics, linear dynamical systems, and the quantum theory of measurement. This volume is organized into six sections encompassing 30 chapters and begins with an introduction to geometric structures, mechanics, and general relativity. It considers an approach to quantum mechanics through deformation of the symplectic structure, giving a striking insight into the correspondence principle. The chapters that follow focus on the gauge invariance of the Einstein field, group treatment of the space of orbits in the Kepler problem, and stable configurations in nonlinear problems arising from physics. This book is intended for researchers and graduate students in theoretical physics, mechanics, control and system theory, and mathematics. It will also be profitably read by philosophers of science and, to some extent, by persons who have a keen interest in basic questions of contemporary mechanics and physics and some background in the physical and mathematical sciences.

Introduction to Global Variational Geometry

1st Edition
Volume 22
April 1, 2000
Demeter Krupka
English
eBook
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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

Introduction to Global Variational Geometry

1st Edition
Volume 20
April 1, 2000
Demeter Krupka
English
eBook
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Introduction to Global Variational Geometry

1st Edition
Volume 23
April 1, 2000
Demeter Krupka
English
eBook
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Axiomatic Projective Geometry

2nd Edition
May 12, 2014
A. Heyting
N. G. De Bruijn + 2 more
English
eBook
9 7 8 1 4 8 3 2 5 9 3 1 4

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

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Books in Geometry

Crystal Symmetries

Topology and Geometry for Physicists

Eigenvalues in Riemannian Geometry

Groups & Geometric Analysis

Semi-Riemannian Geometry With Applications to Relativity

Dynamical Systems and Microphysics

Introduction to Global Variational Geometry

Introduction to Global Variational Geometry

Introduction to Global Variational Geometry

Axiomatic Projective Geometry