TY  - BOOK
AU  - Bejancu,Aurel
AU  - Farran,Hani Reda
ED  - SpringerLink (Online service)
TI  - Foliations and Geometric Structures
T2  - Mathematics and Its Applications
SN  - 9781402037207
U1  - 516.36 23
PY  - 2006///
CY  - Dordrecht
PB  - Springer Netherlands
KW  - MATHEMATICS
KW  - GEOMETRY
KW  - GLOBAL DIFFERENTIAL GEOMETRY
KW  - ALGEBRAIC TOPOLOGY
KW  - MATHEMATICAL PHYSICS
KW  - DIFFERENTIAL GEOMETRY
KW  - MATHEMATICAL METHODS IN PHYSICS
N1  - Geometry of Distributions on a Manifold -- Structural and Transversal Geometry of Foliations -- Foliations on Semi-Riemannian Manifolds -- Parallel Foliations -- Foliations Induced by Geometric Structures -- A Gauge Theory on a Vector Bundle
N2  - 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
UR  - http://dx.doi.org/10.1007/1-4020-3720-1
ER  -