Extrinsic geometry describes houses of foliations on Riemannian manifolds that are expressed when it comes to the second one basic type of the leaves. The authors of Topics in Extrinsic Geometry of Codimension-One Foliations in achieving a technical travel de strength, with the intention to bring about very important geometric results.
The Integral Formulae, brought in bankruptcy 1, is an invaluable for difficulties comparable to: prescribing larger suggest curvatures of foliations, minimizing quantity and effort outlined for vector or airplane fields on manifolds, and life of foliations whose leaves get pleasure from given geometric houses. The fundamental Formulae steams from a Reeb formulation, for foliations on area types which generalize the classical ones. For a unique auxiliary features the formulae contain the Newton variations of the Weingarten operator.
The critical subject of this e-book is Extrinsic Geometric circulate (EGF) on foliated manifolds, that could be a device for prescribing extrinsic geometric houses of foliations. To increase EGF, one wishes Variational Formulae, printed in bankruptcy 2, which expresses a transformation in several extrinsic geometric amounts of a set foliation lower than leaf-wise edition of the Riemannian constitution of the ambient manifold. bankruptcy three defines a basic thought of EGF and stories the evolution of Riemannian metrics alongside the trajectories of this flow(e.g., describes the short-time lifestyles and area of expertise thought and estimate the maximal life time).Some detailed options (called Extrinsic Geometric Solutions) of EGF are offered and are of serious curiosity, on account that they supply Riemannian constructions with very specific geometry of the leaves.
This paintings is geared toward those that be interested within the differential geometry of submanifolds and foliations of Riemannian manifolds.
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