Differential and Riemannian geometry

This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology.

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory.

This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular.

A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold.

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics.

In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be overemphasized.

Enumerative geometry is a core area of algebraic geometry that dates back to Apollonius in the second century BCE.

This book is an introductory text on Differential Geometry presented in tensorial approach.

Several important problems arising in Physics, Differential Geometry and other topics lead to consider semilinear variational equations of strongly indefinite type and a great deal of work has been devoted to their study.

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms.

This volume explores the interplay between mathematical and physical research and the interactions of twentieth-century scientists within their academic communities.

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

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories?

This book illustrates the broad range of Jerry Marsden's mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective.

Soviet citizens can buy Monastyrsky's biography of Riemann for eleven kopeks.

This book is intended to meet the need for a text introducing advanced students in mathematics, physics, and engineering to the field of differential geometry.

This book is intended to meet the need for a text introducing advanced students in mathematics, physics, and engineering to the field of differential geometry.

The book is designed chiefly for the use of students and teachers.

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors.

The Mathematical Works of J.

In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion.

This book is meant to be an introduction to Riemannian geometry.

This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry.

Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space.

Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry.

The author's lectures, "e;Contact Manifolds in Riemannian Geometry,"e; volume 509 (1976), in the Springer-Verlag Lecture Notes in Mathematics series have been out of print for some time and it seems appropriate that an expanded version of this material should become available.

This book is based on the full year Ph.

The main aim of this book is to introduce Lie groups and allied algebraic and geometric concepts to a robotics audience.

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title.

From the Preface: "e;This book was written for the active reader.

This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature.

After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit- ful again.

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par- tition of M into curves, i.

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis.

This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu- larities of stable differentiable mappings.

Experience gained during a ten-year long involvement in modelling, program- ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in- dispensable.

This book provides an upto date information on metric, connection and curva- ture symmetries used in geometry and physics.

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This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties.

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors.

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In recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics-in particular, in string theory.

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

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.

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems.

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems.