By Aurel Bejancu
This self-contained booklet starts off with the elemental fabric on distributions and foliations. It then steadily introduces and builds the instruments wanted for learning the geometry of foliated manifolds. the most subject of the publication is to enquire the interrelations among foliations of a manifold at the one hand, and the numerous geometric constructions that the manifold might admit nevertheless. between those structures are: affine, Riemannian, semi-Riemannian, Finsler, symplectic, advanced and speak to buildings. utilizing those buildings, the publication provides attention-grabbing periods of foliations whose geometry is particularly wealthy and promising. those contain the periods of: Riemannian, completely geodesic, completely umbilical, minimum, parallel non-degenerate, parallel absolutely - null, parallel in part - null, symmetric, transversally symmetric, Lagrange, absolutely actual and Legendre foliations. a few of these sessions seem for the 1st time within the literature in publication shape. ultimately, the vertical foliation of a vector package deal is used to advance a gauge idea at the overall area of a vector bundle.
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