Differential and Riemannian geometry

This book serves two purposes.

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.

Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications.

This accessible introduction for Ph.

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.

The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry.

The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "e;The Geometry of Hamiltonian Systems"e; which was held at MSRl from June 5 to 16, 1989.

This is the first comprehensive book on information geometry, written by the founder of the field.

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

This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences.

This concise book reviews methods used for gluing space-time manifolds together.

This treatment of differential geometry and the mathematics required for general relativity makes the subject of this book accessible for the first time to anyone familiar with elementary calculus in one variable and with a knowledge of some vector algebra.

This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students.

The book is devoted to the study of the geometrical and topological structure of gauge theories.

In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics.

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.

This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature - gravitational, electromagnetic, strong nuclear, and weak nuclear.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side.

A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.

These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "e;Fundamental Fields and Forces"e; at Imperial College.

This book combines the classical and contemporary approaches to differential geometry.

Rational homotopy is a very powerful tool for differential topology and geometry.

This monograph deals with matrix manifolds, i.

This book collects papers presented in the Invited Workshop, "e;Liutex and Third Generation of Vortex Definition and Identification for Turbulence,"e; from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference.

This textbook provides a coherent, integrated look at various topics from undergraduate analysis.

This book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs.

Es gibt in der Differentialgeometrie von Kurven und FJachen zwei Betrachtungsweisen.

Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area.

This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface.

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry.

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics.

This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r-forms, the orientation of a manifold and the Hodge star operator.

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner.

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Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education.

This book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world's leading theoretical physicists, mathematicians, historians and philosophers of science.

The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry.

The package of Gromov's pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics.

Applications covered include image segmentation, shape analysis, image enhancement, and tracking.

This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school “Variational and PDE Methods in Nonlinear Science”, held in Cetraro (Italy), July 10–14, 2023.

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum.

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.

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry.

2 The authors of these issues involve not only mathematicians, but also speci- alists in (mathematical) physics and computer sciences.