Table of Contents

Preface: why projective?; 1. Introduction; 2. The geometry of the projective line; 3. The algebra of the projective line and cohomology of Diff(S1); 4. Vertices of projective curves; 5. Projective invariants of submanifolds; 6. Projective structures on smooth manifolds; 7. Multi-dimensional Schwarzian derivatives and differential operators; Appendix 1. Five proofs of the Sturm theorem; Appendix 2. The language of symplectic and contact geometry; Appendix 3. The language of connections; Appendix 4. The language of homological algebra; Appendix 5. Remarkable cocycles on groups of diffeomorphisms; Appendix 6. The Godbillon–Vey class; Appendix 7. The Adler–Gelfand–Dickey bracket and infinite-dimensional Poisson geometry; Bibliography; Index.

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A rapid route for graduate students and researchers to the frontiers of research in this evergreen subject, first published in 2005.

Reviews

'… this is an introduction to global projective differential geometry offering felicitous choice of topics, leading from classical projective differential geometry to current fields of research in mathematics and mathematical physics. The reader is guided from simple facts concerning curves and derivatives to more involved problems and methods through a world of inspiring ideas, delivering insights in deep relations. Historical comments as well as stimulating exercises occur frequently throughout the text, making it suitable for teachings.' Zentralblatt MATH