Differential and Riemannian geometry

The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together.

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a developing field now regarded as an essential tool in many areas of pure and applied mathematics.

Complex Finsler metrics appear naturally in complex analysis.

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 textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology.

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.

This book is an elementary introduction to the geometrical methods and notions used in special and general relativity.

This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry.

This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point.

A classic treatment of curvature and Betti numbers from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

The book provides an introduction to Differential Geometry of Curves and Surfaces.

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators.

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics.

This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.

"e;Symplectic Geometric Algorithms for Hamiltonian Systems"e; will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc.

This book gives an advanced overview of several topics in infinite group theory.

Grid technology whose achievements have significant impact on the efficiency of numerical codes still remains a rapidly advancing field of computational and applied mathematics.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature.

This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years.

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge-Ampere and linearized Monge-Ampere equations.

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on "e;canonical"e; Riemannian metrics on smooth manifolds.

Addressing graduate students and researchers in theoretical physics and mathematics, this book presents a new formulation of the theory of gravity.

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This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories.

This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute.

The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective.

The study of minimal surfaces is an important subject in differential geometry, and Nevanlinna theory is an important subject in complex analysis and complex geometry.

This book introduces D-modules and their applications avoiding all unnecessary over-sophistication.

This volume contains the courses and lectures given during the workshop on Differential Geometry and Topology held at Alghero, Italy, in June 1992.

Everything the Power of the World does is done in a circle.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1).

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type.

The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frederic Faure and Masato Tsujii).

New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems.

This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM).

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.

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

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.