Search results
Results From The WOW.Com Content Network
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
In contrast to positively curved varieties such as del Pezzo surfaces, a complex algebraic K3 surface X is not uniruled; that is, it is not covered by a continuous family of rational curves. On the other hand, in contrast to negatively curved varieties such as surfaces of general type, X contains a large discrete set of rational curves ...
Each of the solid tori is then foliated internally, in codimension 1, and the dividing torus surface forms one more leaf. By Novikov's compact leaf theorem , every smooth foliation of the 3-sphere includes a compact torus leaf, bounding a solid torus foliated in the same way.
Every rational variety, including the projective spaces, is rationally connected, but the converse is false. The class of the rationally connected varieties is thus a generalization of the class of the rational varieties. Unirational varieties are rationally connected, but it is not known if the converse holds.
Gneiss, a foliated metamorphic rock. Quartzite, a non-foliated metamorphic rock. Foliation in geology refers to repetitive layering in metamorphic rocks. [1] Each layer can be as thin as a sheet of paper, or over a meter in thickness. [1] The word comes from the Latin folium, meaning "leaf", and refers to the sheet-like planar structure. [1]
Every irreducible complex algebraic curve is birational to a unique smooth projective curve, so the theory for curves is trivial. The case of surfaces was first investigated by the geometers of the Italian school around 1900; the contraction theorem of Guido Castelnuovo essentially describes the process of constructing a minimal model of any smooth projective surface.
Taut foliations are closely related to the concept of Reebless foliation.A taut foliation cannot have a Reeb component, since the component would act like a "dead-end" from which a transverse curve could never escape; consequently, the boundary torus of the Reeb component has no transverse circle puncturing it.
From a foundational perspective, the above theorem is usually used as the definition of (,,). That is, the Chow variety is usually defined as a subvariety of P V k , d , n {\displaystyle \mathbb {P} V_{k,d,n}} , and only then shown to be a fine moduli space for the moduli problem in question.