Differential and Riemannian geometry

This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two.

The object of this book is to introduce the reader to some of the most important techniques of modern global geometry.

Many branches of science and engineering involve applications of mathematical analysis.

This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work.

This is both a textbook and a monograph.

This book deals with the new class of one-dimensional variational problems - the problems with branching solutions.

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations.

This invaluable book contains selected papers of Prof Chuan-Chih Hsiung, renowned mathematician in differential geometry and founder and editor-in-chief of a unique international journal in this field, the Journal of Differential Geometry.

In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry.

Foreword by S S Chern In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds.

This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions.

This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics.

This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira.

This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics.

The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China.

The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds.

This unique book deals with the theory of Rozansky-Witten invariants, introduced by L Rozansky and E Witten in 1997.

This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago.

This volume contains a valuable collection of research articles by active and well-known mathematicians in differential geometry and mathematical physics, contributed to mark Professor Kouei Sekigawa's 60th birthday.

The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations.

The geometry of Hessian structures is a fascinating emerging field of research.

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.

Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century.

This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields.

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective.

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.

This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows.

This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.

This volume contains research and expository papers on recent advances in foliations and Riemannian geometry.

This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems.

This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems.

Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis.

The aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds.

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date.

The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory.

This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications.

Stochastic analysis on Riemannian manifolds without boundary has been well established.

The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.

This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis.

'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers.

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

This volume contains original papers and announcements of recent results presented by the main participants of the 5th International Colloquium on Differential Geometry and its Related Fields (ICDG2016).

A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry - except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y.

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.

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