Proceedings Of The Conference Contemporary Geometry And Related Topics Belgrade June 26 July 2 2005

This volume covers a broad range of topics in modern geometry and related branches of mathematics, physics and visualization. Most of papers give new interesting results in Riemannian and pseudo-Riemannian geometry, various structures on differentiable manifolds, homogenous spaces, submanifolds, Lie algebra cohomology, topology, integrable systems, general relativity, Finsler geometry, geometric invariant theory, links and knots, and noncommutative geometry. There are also papers giving overviews of the recent achievements in some special topics such as Kähler geometry, Minkowski spaces, spectral geometry, quantum groups and Hofer's geometry. This book provides a great chance for interchanging new results and ideas in multidisciplinary studies.

This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).

Althoughsubmanifoldscomplexmanifoldshasbeenanactive?eldofstudyfor many years, in some sense this area is not su?ciently covered in the current literature. This text deals with the CR submanifolds of complex manifolds, with particular emphasis on CR submanifolds of complex projective space, and it covers the topics which are necessary for learning the basic properties of these manifolds. We are aware that it is impossible to give a complete overview of these submanifolds, but we hope that these notes can serve as an introduction to their study. We present the fundamental de?nitions and results necessary for reaching the frontiers of research in this ?eld. There are many monographs dealing with some current interesting topics in di?erential geometry, but most of these are written as encyclopedias, or research monographs, gathering recent results and giving the readers ample usefulinformationaboutthetopics. Therefore, thesekindsofmonographsare attractive to specialists in di?erential geometry and related ?elds and acce- able to professional di?erential geometers. However, for graduate students who are less advanced in di?erential geometry, these texts might be hard to read without assistance from their instructors. By contrast, the general philosophy of this book is to begin with the elementary facts about complex manifolds and their submanifolds, give some details and proofs, and introduce the reader to the study of CR submanifolds of complex manifolds; especially complex projective space. It includes only a few original results with precise proofs, while the others are cited in the reference list.

This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

ICMT-2014, the International Conference on Mathematics Textbook Research and Development, brought together mathematics educators, textbook researchers and developers, and policy makers from different parts of the world to share their research results, development experiences and reform ideas, and discuss issues and directions concerning mathematics textbook research and development. These proceedings contain all the papers presented at the conference, including the plenary presentations and plenary panel, as well as the symposia, research papers, and workshops. This volume provides a comprehensive record of the ICMT-2014 conference and serves as an essential reference for education researchers, practitioners, and policy makers and curriculum developers interested in mathematics textbook research and development.

This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.