Foliations with Degenerate Gauss Maps on P
نویسنده
چکیده
We obtain a classification of codimension one holomorphic foliations on P with degenerate Gauss maps.
منابع مشابه
Volume-minimizing Foliations on Spheres
The volume of a k-dimensional foliation F in a Riemannian manifold Mn is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing the construction by Gluck and Ziller in [4], “singular” foliations by 3-spheres are constructed on round spheres S, as well as a singular foliation by 7-spheres on S, which minimize v...
متن کاملOn the Characterization of Algebraically Integrable Plane Foliations
We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree r of a non-degenerate foliation as above provides the minimum number, r+ 1, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.
متن کاملStability of Foliations Induced by Rational Maps
We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute the...
متن کاملConstant curvature foliations in asymptotically hyperbolic spaces
Let (M, g) be an asymptotically hyperbolic manifold with a smooth conformal compactification. We establish a general correspondence between semilinear elliptic equations of scalar curvature type on ∂M and Weingarten foliations in some neighbourhood of infinity inM . We focus mostly on foliations where each leaf has constant mean curvature, though our results apply equally well to foliations whe...
متن کامل2 4 A ug 2 00 6 The geometry of conformally Einstein metrics with degenerate Weyl tensor
The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a " non-degeneracy " condition on the Weyl tensor W. We investigate the geometry of the foliations arising on conformally Einstein spaces (with Riemannian signature) where thi...
متن کامل