Libros de Geometría, página 3 de 23

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

 ,This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved._,

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kahler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kahler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kahler geometry. Another feature of the book is that we have tried wherever poss

En este libro, Javier Bracho desarrolla la noción moderna de espacio e invita al lector a vivir una serie de experiencias relacionadas con los distintos mundos posibles a partir de los diferentes espacios; experiencias que al principio nos parecen fantasticas y que nos hacen entrar en contacto con la geometria actual.

In the theory of minimal submanifolds, Bernstein''s problem and Plateau''s problem are central topics. This important book presents the DouglasRado solution to Plateau''s problem, but the main emphasis is on Bernstein''s problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons'' work for minimal graphic hypersurfaces, and the author''s own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.This new edition contains the author''s recent work on the LawsonOsserman''s problem for higher codimension, and on Chern''s problem for minimal hypersurfaces in the sphere. Both Chern''s problem and LawsonOsserman''s problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.Readership: Researchers and graduate students in differential geometry.

El propósito de este libro es ofrecer al profesorado y alumnado algunos aspectos de Geometría plana, tratados de forma asequible y fundamentalmente práctica. El profesorado encontrará, en los contenidos teoricos y en las propuestas de ejercicios practicos, un tratamiento no tradicional del estudio de poligonos.

El matemático alemán Felix Klein (1849-1925), aunque más conocido por su sistematización de la geometría no euclidiana, fue también un profesor preocupado por la enseñanza. En este volumen late el entusiasmo de las clases originales de las que proceden-, Klein trata siempre, tal y como comenta en el prologo, "de combinar la intuicion geometrica con la precision de las formulas aritmeticas".

Earl W. Swokowski / Jeffery A. Cole La novena edición de este conocido texto ha sido mejorada, sin modificar la claridad matemática que lo caracteriza, con los siguientes aspectos: la exposición de los temas se ha actualizado para hacer mas facil la comprension de los conceptos matematicos, se han agregado ejercicios que requieren a los estudiantes estimar, aproximar, interpretar un resultado, resumir, hacer un modelo, explorar o encontrar una generalizacion.

TEC/Lazo, AdrianaLa experiencia docente de los autores los llevó a concebir una obra que cubriera de manera integral las diferentes disciplinas de las matemáticas, como son los conocimientos algebraicos, geometricos y de geometria analitica, de tal forma que ni el profesor ni los alumnos tengan la necesidad de utilizar diferentes libros durante el curso escolar. Por ello, esta obra cubre los temas de funciones de geometria analitica, buscando una correlacion logica entre los temas y diferentes disciplinas y conservando un mismo enfoque, formato y grado de dificultad. Contiene una gran cantidad de ejercicios, ademas de otros aspectos didacticos que facilitaran la comprension de lo temas tratados.

Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student.

 ,This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer&ndash,Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang&ndash,Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry._,

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.