Projective Differential Geometry Old and New
by V. Ovsienko, S. Tabachnikov
Publisher: Cambridge University Press 2004
Number of pages: 281
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. This book provides a rapid route for graduate students and researchers to contemplate the frontiers of contemporary research in this classic subject. The authors include exercises and historical and cultural comments relating the basic ideas to a broader context.
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by John Morgan, Gang Tian - American Mathematical Society
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
by Li Ma - Tsinghua University
Contents: Ricci-Hamilton flow on surfaces; Bartz-Struwe-Ye estimate; Hamilton's another proof on S2; Perelman's W-functional and its applications; Ricci-Hamilton flow on Riemannian manifolds; Maximum principles; Curve shortening flow on manifolds.
by Dave Auckly - arXiv
This paper introduced undergraduates to the Atiyah-Singer index theorem. It includes a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
by Aleks Kleyn, Alexandre Laugier - arXiv
In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Contents: Preface; Minkowski Space; Examples of Minkowski Space.