Lecture Notes On Differential Geometry
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Lecture Notes On Differential Geometry
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Author : Prakash Dabhi
language : de
Publisher:
Release Date : 2015-09-01
Lecture Notes On Differential Geometry written by Prakash Dabhi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-01 with categories.
Document from the year 2015 in the subject Mathematics - Geometry, course: Differential Geometry, language: English, abstract: This is a Lecture Notes on a one semester course on Differential Geometry taught as a basic course in all M.Sc./M.S. programmes in Mathematics. This consists normally of curve theory leading up to fundamental theorem of space curves as well as the Gauss theory of surfaces covering first fundamental form, second fundamental form, Gaussian curvature, geodesic and Gauss Bonnet theorem. This Lecture Notes is based on lectures I have given to M.Sc. Mathematics students of Sardar Patel University, Vallabh Vidyanagar, India. Here are the salient features of the Lecture Notes. Proofs of all assertions are completely given in a lucid student friendly manner. A large number of solved exercises are included. All these are to facilitate self study by the students. I have also adopted the modern approach to develop the classical topics treated here. The Lecture Notes is highly influenced by the approach adopted in Elementary Differential Geometry by Andrew Pressley and Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo. I am indebted to these authors whose work have influenced my learning of the subject as well as the preparation of this Lecture Notes. I hope this little book would invite the students to the subject of Differential Geometry and would inspire them to look to some comprehensive books including those mentioned above.
Differential Geometry In The Large
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Author : Heinz Hopf
language : en
Publisher: Springer
Release Date : 2003-07-01
Differential Geometry In The Large written by Heinz Hopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .
Lecture Notes On Differential Geometry Paperback
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Author : Jin-Oh Hyun
language : en
Publisher:
Release Date : 2006-03-01
Lecture Notes On Differential Geometry Paperback written by Jin-Oh Hyun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with categories.
Differential Geometry
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Author : Robert Geroch
language : en
Publisher: Minkowski Institute Press
Release Date : 2013-10-14
Differential Geometry written by Robert Geroch and has been published by Minkowski Institute Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Science categories.
Robert Geroch's lecture notes on differential geometry reflect his original and successful style of teaching - explaining abstract concepts with the help of intuitive examples and many figures. The book introduces the most important concepts of differential geometry and can be used for self-study since each chapter contains examples and exercises, plus test and examination problems which are given in the Appendix. As these lecture notes are written by a theoretical physicist, who is an expert in general relativity, they can serve as a very helpful companion to Geroch's excellent "General Relativity: 1972 Lecture Notes."
Lecture Notes On Elementary Topology And Geometry
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Author : I.M. Singer
language : en
Publisher: Springer
Release Date : 2015-05-28
Lecture Notes On Elementary Topology And Geometry written by I.M. Singer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Mathematics categories.
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
Lecture Notes On Geometrical Aspects Of Partial Differential Equations
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Author : V V Zharinov
language : en
Publisher: World Scientific
Release Date : 1992-03-26
Lecture Notes On Geometrical Aspects Of Partial Differential Equations written by V V Zharinov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-26 with Mathematics categories.
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.
A Course In Differential Geometry
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Author : Thierry Aubin
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
A Course In Differential Geometry written by Thierry Aubin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This textbook for second-year graduate students is an introduction to differential geometry with principal emphasis on Riemannian geometry. The author is well-known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
Lectures On Differential Geometry
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Author : Richard M. Schoen
language : en
Publisher:
Release Date : 1994
Lectures On Differential Geometry written by Richard M. Schoen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Geometry, Differential categories.
Modern Differential Geometry For Physicists
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Author : Chris J. Isham
language : en
Publisher: World Scientific
Release Date : 1999
Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
"The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects".Mathematical Reviews"This book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism". Mathematical Reviews
Introduction To Differential Geometry
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Author : Joel W. Robbin
language : en
Publisher: Springer Nature
Release Date : 2022-01-12
Introduction To Differential Geometry written by Joel W. Robbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-12 with Mathematics categories.
This 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. The 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. An 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.