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...

We consider holomorphic maps defined in an annulus around R/Z C/Z. E. Risler proved that a generic analytic family of such fζ contains Brjuno rotation f0(z)=z+α, all are conjugate to this form codimension-1 submanifold near f0. In paper, we obtain the Risler's result as corollary following construction. introduce renormalization operator on space univalent neighborhood R/Z. prove is hyperbolic,...

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is th...

We construct 1-parameter families of non-periodic embedded minimal surfaces infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each our converges to foliation \mathbb{R}$ by $T$. These then lift $\mathbb{R}^3$ that are periodic horizontal directions but not the vertical direction. In language crystallography, construction can be interpreted as disordered stacking layers p...

To optimize the prediction of structural geological conditions in underground as data collected at surface, due to usual great uncertainties involved, we discuss new perspectives for construction models, bearing mind common doubts involved and their implications safety infrastructure works, mining, etc. This paper presents a statistical simulation applied measures (dip-dip direction) obtained f...

Let $$g_t$$ be a smooth 1-parameter family of negatively curved metrics on closed hyperbolic 3-manifold M starting at the metric. We construct foliations Grassmann bundle $$Gr_2(M)$$ tangent 2-planes whose leaves are (lifts of) minimal surfaces in $$(M,g_t)$$ . These deformations foliation by totally geodesic planes projected down from universal cover $${\mathbb {H}}^3$$ Our construction contin...

We obtain the following two results through foliation theoretic approaches including a review of Lawson’s construction of a codimension-one foliation on the 5-sphere: 1) The standard contact structure on the 5-sphere deforms to ‘Reeb foliations’. 2) We define a 5-dimensional Lutz tube which contains a plastikstufe. Inserting it into any contact 5-manifold, we obtain a contact structure which vi...