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The level of these problems is quite varied, ranging from those handling simple properties to others that need sophisticated tools. Similarly, manifolds are supposed to be Hausdorff and second countable, though a section is included analysing what happens when these properties fail, aimed at a better understanding of the meaning of such properties. The Einstein summation convention is used. Chapter 7 provides a selection of the theorems and definitions used throughout the book, but restricted to those whose terminology could be misleading for the lack of universal acceptance.
Moreover, to solve some types of problems, certain ix x Preface definitions and notations should be precisely fixed; recalling the exact statement of some theorems is often convenient in practice as well. However, this chapter has by no means the intention of being either a development or a digest of the theory. Chapter 8 offers a collection of formulae and tables concerning spaces and groups frequent in differential geometry. As in Chapter 7, no effort to be exhaustive has been attempted.
We hope the book will render a good service to teachers and students of differential geometry and related topics. While no reasonable effort has been spared to ensure accuracy and precision, the attempt of writing such a book necessarily will contain misprints, and probably some errors. Any corrections, suggestions or comments helping to improve future editions will be highly appreciated. We are indebted to Arturo Quijada Arteaga for his excellent work in the graphics. Implicit Map Theorem. Quotient Manifolds. Tensor Fields. Exterior Product. Interior Product.
Differential Ideals. Orientation-preserving maps.
Analysis and Algebra on Differentiable Manifolds | dienarthlartipsmes.ga
His current interests are in differential geometry and Lie groups theory, and specifically in Riemannian, Kahler, hyper-Kahler and Spin 9 structures possessing rich groups of symmetries. Outside of mathematics, his main interests are history and bicycle travels. Subscribe now to be the first to hear about specials and upcoming releases. South Pacific. Title Author. Trade Paperback 1. Description of this Book This is the second edition of this best selling problem book for students, now containing over completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.
Professors Gadea, Masque and Mykytyuk have produced a workbook that appears to be an equally useful supplement for either a primarily theoretical or an application oriented course on differential geometry or differential topology.
This exceptional workbook puts me in mind of a mightily enhanced Schaum's outline, and I have an abiding respect for the educational value of the Schaum's series. A mastery of the material in this workbook would, I think, stand as compelling evidence of a very strong grounding in the fundamentals of modern differential geometry and related areas. The authors deserve kudos for this admirable contribution to Springer's Problem Books in Mathematics series.
It is bound to be an excellent learning tool for students of differential geometry and differential topology at any level as well as a handy reference for experts in these fields.
In the gallery of scientific self-help literature, in which kitsch abounds, this workbook certainly qualifies as high art. One thing for sure, when next I teach a course in differential geometry or differential topology, I am certainly going to recommend this workbook as a supplementary text. Author's Bio Professor Pedro M. This preview is indicative only.