The book is self-contained. It starts with the basic material on
distributions and foliations. Then it proceeds to gradually
introduce and build 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 one hand,
and the many geometric structures that the manifold may admit on
the other hand. Among these structures we mention: 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 a 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 book will be of interest to graduate students who want to be
introduced to the geometry of foliations, to researchers working on
foliations and geometric structures, and to physicists interested
in gauge theories.
General
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