This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
This book covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. It treats in detail classical results on the relations between curvature and topology. The book features numerous exercises with full solutions and a series of detailed examples are picked up repeatedly to illustrate each new definition or property introduced.
The school, the book This book is based on lectures given by the authors of the various chapters in a three week long CIMPA summer school, held in Sophia-Antipolis (near Nice) in July 1992. The first week was devoted to the basics of symplectic and Riemannian geometry (Banyaga, Audin, Lafontaine, Gauduchon), the second was the technical one (Pansu, Muller, Duval, Lalonde and Sikorav). The final week saw the conclusion ofthe school (mainly McDuffand Polterovich, with complementary lectures by Lafontaine, Audin and Sikorav). Globally, the chapters here reflect what happened there. Locally, we have tried to reorganise some ofthe material to make the book more coherent. Hence, for instance, the collective (Audin, Lalonde, Polterovich) chapter on Lagrangian submanifolds and the appendices added to some of the chapters. Duval was not able to write up his lectures, so that genuine complex analysis will not appear in the book, although it is a very current tool in symplectic and contact geometry (and conversely). Hamiltonian systems and variational methods were the subject of some of Sikorav's talks, which he also was not able to write up. On the other hand, F. Labourie, who could not be at the school, wrote a chapter on pseudo-holomorphic curves in Riemannian geometry.
Based on four years of research in the French-Canadian press of the 1840s and the private papers of the main French-Canadian politicians, British officials, and Roman Catholic religious leaders, this book describes in rich and lively detail the conflict of French Canada's priests and politicians around the central issue of their people's relation to the British Crown during that period. Confederation in 1867, modern Canada, and the current tempest in French Canada cannot adequately be understood without constant reference to these men of the 1840s and the political and religious ideologies they represented. Indeed, it was in their enmities, in their friendships and loyalties that were laid the strongbi-national foundations of what Etienne Parent foresaw as 'une grande nationalité canadienne assez forte pour se protéger elle-même et vivre de sa propre vie.
The acclaimed series The Collected Writings of Jean-Jacques Rousseau concludes with a volume centering on Emile (1762), which Rousseau called his “greatest and best book.” Here Rousseau enters into critical engagement with thinkers such as Locke and Plato, giving his most comprehensive account of the relation between happiness and citizenship, teachers and students, and men and women. In this volume Christopher Kelly presents Allan Bloom’s translation, newly edited and cross-referenced to match the series. The volume also contains the first-ever translation of the first draft of Emile, the “Favre Manuscript,” and a new translation of Emile and Sophie, or the Solitaries. The Collected Writings of Rousseau Roger D. Masters and Christopher Kelly, series editors 1. Rousseau, Judge of Jean-Jacques: Dialogues 2. Discourse on the Sciences and Arts (First Discourse) and Polemics 3. Discourse on the Origins of Inequality (Second Discourse) Polemics, and Political Economy 4. Social Contract, Discourse on the Virtue Most Necessary for a Hero, Political Fragments, and Geneva Manuscript 5. The Confessions and Correspondence, Including the Letters to Malesherbes 6. Julie, or the New Heloise: Letters of Two Lovers Who Live in a Small Town at the Foot of the Alps 7. Essay on the Origin of Languages and Writings Related to Music 8. The Reveries of the Solitary Walker, Botanical Writings, and Letter to Franquières 9. Letter to Beaumont, Letters Written from the Mountain 10. Letter to D’Alembert and Writings for the Theater 11. The Plan for Perpetual Peace, On the Government of Poland, and Other Writings on History and Politics 12. Autobiographical, Scientific, Religious, Moral, and Literary Writings 13. Emile or On Education (Includes Emile and Sophie; or The Solitaries)
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.