However since a Riemannian manifold is even initially a subtle object appealing to highly non-natural concepts the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way fo... Lees meer.

From the preface. Many years have passed since the first edition. However the encouragements of various readers and friends have persuaded us to write this third edition. During these years Riemannian Geometry has undergone many dramatic developments. Here is not the... Lees meer.

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 i... Lees meer.

Unlike many other texts on differential geometry this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds differential forms metrics and cu... Lees meer.

This text on Riemannian geometry and geometric analysis is written for graduates and reseachers and includes material new to the late 1990s on Ginzburg-Landau Seibert-Witten functionals spin geometry and Dirac operators.... Lees meer.

Recent developments in the field of differential geometry have been so extensive that a new book with particular emphasis on current work in Riemannian geometry is clearly necessary. This new text brilliantly serves that purpose and includes an elementary account of twi... Lees meer.

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 defin... Lees meer.

Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry which plays for these systems the same role as Euclidean geometry does for linear systems.... Lees meer.

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles a... Lees meer.

Honoring Andrei Agrachev s 60th birthday this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian g... Lees meer.

This monograph deals with the Riemannian geometry of both symplectic and contact manifolds with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1 which examines the general theory of symplectic manifolds. P... Lees meer.

Non-Riemannian Geometry deals basically with manifolds dominated by the geometry of paths developed by the author Luther Pfahler Eisenhart and Oswald Veblen who were faculty colleagues at Princeton University during the early twentieth century. Eisenhart played an a... Lees meer.

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 tha... Lees meer.

Developments in topology and analysis have led to the creation of various lines of investigation in differential geometry. This title presents the background context and main techniques of three such lines by means of surveys by some of the leading researchers. It is s... Lees meer.

Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis geometry and physics. The equations studied here are of the well-known Yamabe type. They involve Schr dinger... Lees meer.