Foliations and Geometric Structures

The theory of foliations of manifolds was created in the forties of the last century by Ch. Ehresmann and G. Reeb ER44]. Since then, the subject has enjoyed a rapid development and thousands of papers investigating foliations have appeared. A list of papers and preprints on foliations up to 1995 can be found in Tondeur Ton97]. Due to the great interest of topologists and geometers in this rapidly ev- ving theory, many books on foliations have also been published one after the other. We mention, for example, the books written by: I. Tamura Tam76], G. Hector and U. Hirsch HH83], B. Reinhart Rei83], C. Camacho and A.L. Neto CN85], H. Kitahara Kit86], P. Molino Mol88], Ph. Tondeur Ton88], Ton97], V. Rovenskii Rov98], A. Candel and L. Conlon CC03]. Also, the survey written by H.B. Lawson, Jr. Law74] had a great impact on the de- lopment of the theory of foliations. So it is natural to ask: why write yet another book on foliations? The answerisverysimple.Ourareasofinterestandinvestigationaredi'erent.The main theme of this book is to investigate the interrelations between foliations of a manifold on one hand, and the many geometric structures that the ma- foldmayadmitontheotherhand.Amongthesestructureswemention: a'ne, Riemannian, semi-Riemannian, Finsler, symplectic, and contact structures.