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1.
˜The œNovikov conjecture : geometry and algebra / by Kreck,, Matthias, Publication: Basel ; | Boston : BirkhŁauser, 2005 . xv, 266 p. ; 24 cm. Date: 2005 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

2.
An Introduction to geometrical physics / by Aldrovandi, R. Publication: [S.l.] : World Scientific Publishing Company, 1995 . 699 p. ; , This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students. 22 cm. Date: 1995 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

3.
An introduction to symplectic geometry by Berndt, Rolf. Publication: [S.l.] American Mathematical Society 2000 . 195 p. , Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, K�hler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometr 26 cm. Date: 2000 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

4.
Analysis and geometry on groups by Varopoulos, N. Publication: Cambridge Cambridge University Press 2008 . xii, 155 pages , Originally published: 1992. 24 cm. Date: 2008 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

5.
Beweismethoden der differentialgeometrie im grossen by Huck,, H. Publication: [S.l.] Springer 1973 . 172 p. 24 cm. Date: 1973 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

6.
Compact riemann surfaces : an introduction to contemporary mathematics / by Jost,, Jûrgen. Publication: [S.l.] : Springer, 2006 . 282 p. ; , Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmǂller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation. 24 cm. Date: 2006 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

7.
Complex Analysis by Eells, J., Publication: New York Springer 2008 . 1 online resource. Date: 2008 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

8.
Complex geometry : an introduction / by Huybrechts, Daniel. Publication: Berlin ; | New York : Springer, 2005 . xii, 309 p. : 24 cm. Date: 2005 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

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Differential geometry and lie groups for physicists by Fecko, Marián. Publication: Cambridge Cambridge University Press 2010 . pages cm. , Originally published: 2006. Date: 2010 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

11.
Differential geometry and physics proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics, Tianjin, China, 20-26 August 2005 by Ge, M. L. Publication: Hackensack, NJ World Scientific 2006 . xviii, 522 pages 24 cm. Date: 2006 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

12.
Differential geometry and symmetric spaces by Helgason, Sigurdur Publication: Providence American Mathematical Society 2001 . 487 p. , Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there are now many competing texts, the chapters on differential geometry and Lie groups continue to be among the best treatments of the subjects available. There is also a well-developed treatment of Cartan's classification and structure theory of symmetric spaces. The last chapter, on functions on symmetric spaces, remains an excellent introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis. This text is rightly called a classic. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces. 24 cm. Date: 2001 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

13.
Differential geometry and topology with a view to dynamical systems by Burns, Keith, Publication: Boca Raton CRC Press 2005 . ix, 389 pages 24 cm. Date: 2005 Availability: No items available:

14.
Differential geometry, lie groups, and symmetric spaces by Helgason, Sigurdur. Publication: Providence (R. I.) American Mathematical Society 2001 . 641 p. , The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $mathbf{C}$ and Cartan's classification of simple Lie algebras over $mathbf{R}$. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book. For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis. 27 cm. Date: 2001 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

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Equivalence, invariants, and symmetry by Olver, Peter J. Publication: Cambridge Cambridge University Press 2009 . pages , Originally published: 1995. cm. Date: 2009 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

17.
Foundations of differential geometry / by Kobayashi,, Shoshichi, Publication: New York : Wiley, 1996 . 2 volumes ; , "A Wiley-Interscience publication." 23 cm. Date: 1996 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

18.
Fundamentals of differential geometry by Lang,, Serge. Publication: [S.l.] Springer 2001 . 540 p. , This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER. 24 cm. Date: 2001 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

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Geometric asymptotics by Guillemin, Victor. Publication: Providence, R.I. American Mathematical Society 1977 . 480 p. , Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years--the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence. Chapters included in this book are: Chapter I, Introduction. The method of stationary phase; Appendix I, Morse's lemma and some generalizations; Chapter II, Differential operators and asymptotic solutions; Chapter III, Geometrical optics; Chapter IV, Symplectic geometry; Chapter V, Geometric quantization; Chapter VI, Geometric aspects of distribution; Appendix to Chapter VI, The Plancherel formula for the complex semisimple Lie groups; Chapter VII, Compound Asymptotics; Appendix II, Various functorial constructions; Index. 26 cm. Date: 1977 Availability: Items available: La bibliothèque des Sciences Exactes et Naturelles (1),

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