Kdhler-Einstein Metrics and Integral Invariants (Lecture Notes in Mathematics, #1314)
by Akito Futaki
Conformal Geometry of Surfaces in S4 and Quaternions (Lecture Notes in Mathematics, #1772)
by Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, and Ulrich Pinkall
The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Backlund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
Differential Geometry (Graduate Texts in Mathematics, #166)
by R.W. Sharpe
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more...
Homogeneity of Equifocal Submanifolds (Berichte aus der Mathematik)
by Ulrich Christ
Optimal control of differential equations (Lecture Notes in Pure and Applied Mathematics, #160)
"Based on the International Conference on Optimal Control of Differential Equations held recently at Ohio University, Athens, this Festschrift to honor the sixty-fifth birthday of Constantin Corduneanu an outstanding researcher in differential and integral equations provides in-depth coverage of recent advances, applications, and open problems relevant to mathematics and physics. Introduces new results as well as novel methods and techniques!"
Theorie Elementaire Et Pratique de La Commande Par Les Regimes Glissants (Mathematiques Et Applications, #55)
by Pierre Lopez and Ahmed Sac/D Nouri
Sources of Hyperbolic Geometry (History of Mathematics, #10)
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Labachevsky seems long overdue - not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathemat...
Multivariable Calculus and Mathematica (R)
by Kevin R. Coombes, Ronald L. Lipsman, and Jonathan M. Rosenberg
Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an oppor...
Boundary Element Topics
The so-called boundary element methods BEM, i.e. finite element approxima- tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re- sults and decisive new develop...
Surgical Methods in Rigidity (Tata Institute Lectures on Mathematics and Physics S.)
by F. Thomas Farrell
This book is an introduction to the topological rigidity theorem for compact non-positively curved Riemannian manifolds. It contains a quick informal account of the background material from surgery theory and controlled topology prerequesite to this result. It is intended for researchers and advanced graduate students in both differential geometry and topology. This book is the content of a course given by the author at TIFR in 1993.
Dynamics And Symmetry (Icp Advanced Texts In Mathematics, #3)
by Michael Field
This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian...
Smooth Quasigroups and Loops (Mathematics and Its Applications, #492)
by Lev Sabinin
During the last twenty-five years quite remarkable relations between nonasĀ sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebra...
Introduction to Hyperbolic Geometry (Universitext)
by A. Ramsay and R D Richtmyer
This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes pro...
Theory of Control Systems Described by Differential Inclusions (Springer Tracts in Mechanical Engineering)
by Zhengzhi Han, Xiushan Cai, and Jun Huang
This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Lure systems. They also introduce the elemental theory of finite dimensional differential inclusions, and the properties and designs of the control systems described by differential incl...
Non-linear Partial Differential Operators and Quantization Procedures (Lecture Notes in Mathematics, #1037)
Discrete Groups, Expanding Graphs and Invariant Measures (Progress in Mathematics, #125)
by Alex Lubotzky
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs ("expanders"). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for vari...
Morse Theory and Floer Homology (Universitext)
by Michele Audin and Mihai Damian
This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold.The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse com...
Geometric Analysis is one of the most active research fields nowadays. The interplay between geometric and analytic techniques is at the core of recent remarkable advances in Differential Geometry and Topology. However, the majority of the monographs and books on the subject focus on intrinsic Riemannian Geometry techniques and applications. A systematic treatment of problems involving the extrinsic curvature of submanifolds is still missing in the literature. In particular, up to our knowledge,...
The Many Faces of Maxwell, Dirac and Einstein Equations (Lecture Notes in Physics, #722)
by Waldyr A. Rodrigues and Edmundo C. de Oliveira
This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.
Metric Geometry of Locally Compact Groups (EMS Tracts in Mathematics)
by Yves Cornulier