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Isoparametric hypersurfaces in complex hyperbolic spaces  [PDF]
Jose Carlos Diaz-Ramos,Miguel Dominguez-Vazquez,Victor Sanmartin-Lopez
Mathematics , 2015,
Abstract: We classify isoparametric hypersurfaces in complex hyperbolic spaces.
Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces  [PDF]
J. Carlos Diaz-Ramos,Miguel Dominguez-Vazquez
Mathematics , 2010,
Abstract: We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
Codimension 1 Mukai foliations on complex projective manifolds  [PDF]
Carolina Araujo,Stéphane Druel
Mathematics , 2014,
Abstract: In this paper we classify codimension 1 Mukai foliations on complex projective manifolds
Polar foliations on quaternionic projective spaces  [PDF]
Miguel Dominguez-Vazquez,Claudio Gorodski
Mathematics , 2015,
Abstract: We classify irreducible polar foliations of codimension $q$ on quaternionic projective spaces $\mathbb H P^n$, for all $(n,q)\neq(7,1)$. We prove that all irreducible polar foliations of any codimension (resp. of codimension one) on $\mathbb H P^n$ are homogeneous if and only if $n+1$ is a prime number (resp. $n$ is even or $n=1$). This shows the existence of inhomogeneous examples of codimension one and higher.
Isotrivial unfoldings and structural theorems for foliations on Projective spaces  [PDF]
Federico Quallbrunn
Mathematics , 2015,
Abstract: Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then applied to obtain information on the structure of foliations on projective spaces.
Transversely projective holomorphic foliations with singularities  [PDF]
Bruno Scardua
Mathematics , 2004,
Abstract: We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of the generic models of codimension one foliations on compact manifolds of dimension $\ge 3$.
Foliations on complex projective surfaces  [PDF]
Marco Brunella
Mathematics , 2002,
Abstract: These are lecture notes of a course given in Pisa, SNS, in february 2002. They provide a classification of holomorphic foliations of nongeneral type on compact Kaehler surfaces.
Riemannian foliations of projective space admitting complex leaves  [PDF]
Thomas Murphy
Mathematics , 2012,
Abstract: Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian foliations of any open subset of $\mathbb{P}^n$ of codimension one. As a consequence there is no Riemannian foliation of the projective plane by Riemann surfaces, even locally. We determine how a complex submanifold may arise as an exceptional leaf of a non-trivial singular Riemannian foliation of maximal dimension. Gray's tube formula is applied to obtain a volume bound for certain holomorphic curves of complex quadrics.
Dynamics of Singular Holomorphic Foliations on the Complex Projective Plane  [PDF]
Saeed Zakeri
Mathematics , 1998,
Abstract: This manuscript is an introduction to the theory of holomorphic foliations on the complex projective plane. Historically the subject has emerged from the theory of ODEs in the complex domain and various attempts to solve Hilbert's 16th Problem, but with the introduction of complex algebraic geometry, foliation theory and dynamical systems, it has now become an interesting subject of its own.
Transversely Lie holomorphic foliations on projective spaces  [PDF]
A. C. Mafra,B. Scardua
Mathematics , 2008,
Abstract: We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection of codimension one foliations given by closed one-forms with simple poles. If there is only one singularity in a suitable affine space, then the foliation is induced by a linear diagonal vector field.
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