Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups (Cambridge Tracts in Mathematics, Series Number 165)

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. Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors'main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject. Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. This book provides a rapid route for graduate students and researchers to the frontiers of contemporary research in this evergreen subject. Exercises play a prominent role: historical and cultural comments relate the basic notions to a broader context The authors explore connections between classical projective differential geometry & contemporary mathematics & mathematical physics, offering new results & new proofs to classic theorems. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, & more