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This self-contained book starts with the basic material on distributions and foliations. It then gradually introduces and builds the tools needed for studying the geometry of foliated manifolds. The main theme of the book is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand. Among these structures are: affine, Riemannian, semi-Riemannian, Finsler, symplectic, complex and contact structures. Using these structures, the book presents interesting classes of foliations whose geometry is very rich and promising. These include the classes of: Riemannian, totally geodesic, totally umbilical, minimal, parallel non-degenerate, parallel totally - null, parallel partially - null, symmetric, transversally symmetric, Lagrange, totally real and Legendre foliations. Some of these classes appear for the first time in the literature in book form. Finally, the vertical foliation of a vector bundle is used to develop a gauge theory on the total space of a vector bundle.
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.
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.