{"product_id":"introduction-to-differential-geometry-paperback-1","title":"Introduction to Differential Geometry - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eJoel W. Robbin\u003c\/b\u003e (Author), \u003cb\u003eDietmar A. Salamon\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThis textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.\u003c\/p\u003e\u003cp\u003eThe first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor.\u003c\/p\u003e \u003cp\u003eAn additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.\u003cbr\u003e\u003c\/p\u003e \u003cp\u003eThe first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor.\u003c\/p\u003e \u003cp\u003eAn additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.\u003c\/p\u003e\u003cb\u003eThe Authors\u003c\/b\u003e\u003cbr\u003e​​\u003cb\u003eJoel W. Robbin\u003c\/b\u003e, Professor emeritus, University of Wisconsin-Madison, Department of Mathematics.\u003cbr\u003e\u003cb\u003eDietmar A. Salamon\u003c\/b\u003e, Professor emeritus, Eidgenössische Technische Hochschule Zürich (ETHZ), Departement Mathematik.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eJoel Robbin\u003c\/b\u003e was born in Chicago in 1941 and completed his PhD at Princeton University in 1965 under the direction of Alonzo Church. After a postdoctoral position in Princeton he took up an Assistant Professorship at the University of Wisconsin-Madson in 1967, where he became full Professor in 1973.\u003cbr\u003eJoel Robbin began his research in mathematical logic (and wrote a text book on this subject) and later moved on to dynamical systems and symplectic topology. In 1970 he proved a conjecture by Stephen Smale which asserts that Axiom A implies structural stability. His publications include a book on \"Matrix Algebra\" and joint book with Ralph Abraham on \"Transversal Mappings and Flows\".\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eHe is a Fellow of the American Mathematical Society.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eDietmar Salamon\u003c\/b\u003e was born in Bremen in 1953 and completed his PhD at the University of Bremen in 1982 under the direction of Diederich Hinrichsen. After postdoctoral positions in Madison and Zurich, he took up a position at the University Warwick in 1986, and moved to ETH Zurich in 1998, where he has been emeritus since 2018. His field of research is symplectic topology and related subjects. \u003c\/p\u003e\u003cp\u003eHe was an invited speaker at the ECM 1992 in Paris, at the ICM 1994 in Zurich, and at the ECM 2000 in Barcelona. He delivered the Andrejewski Lectures in Goettingen (1998) and at the Humboldt Unversity Berlin (2005), and the Xth Lisbon Summer Lectures in Geometry (2009). \u003c\/p\u003e\u003cp\u003eHe is the author of several textbooks and research momgraphs including two joint books with Dusa McDuff entitled \"Introduction to Sympectic Topology\" and \"J-holomorphic Curves and Symplectic Topology\" for which they were jointly awarded the 2017 Leroy P Steele Prize for Mathematical Exposition. He is a Fellow of the American Mathematical Society and a member of the Academia Europaea.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 418\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.88 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e January 13, 2022\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337133900025,"sku":"9783662643396","price":129.58,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/QlliemlIS09RTWhhT2I2Nlp0ZmFIUT09.webp?v=1769675111","url":"https:\/\/bookscloud.io\/products\/introduction-to-differential-geometry-paperback-1","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}