By Jorge Vitório Pereira, Luc Pirio

This publication takes an in-depth examine abelian kin of codimension one webs within the advanced analytic environment. In its classical shape, internet geometry is composed within the research of webs as much as neighborhood diffeomorphisms. an important a part of the speculation revolves round the suggestion of abelian relation, a selected form of practical relation one of the first integrals of the foliations of an online. major focuses of the ebook contain what number abelian kinfolk can an online hold and which webs are wearing the maximal attainable variety of abelian family members. The e-book bargains entire proofs of either Chern’s certain and Trépreau’s algebraization theorem, together with the entire helpful necessities that transcend easy advanced research or easy algebraic geometry. lots of the examples identified modern of non-algebraizable planar webs of maximal rank are mentioned intimately. A historic account of the algebraization challenge for maximal rank webs of codimension one is usually presented.

**Read Online or Download An Invitation to Web Geometry PDF**

**Similar differential geometry books**

**Transformation Groups in Differential Geometry**

Given a mathematical constitution, one of many simple linked mathematical items is its automorphism workforce. the item of this booklet is to provide a biased account of automorphism teams of differential geometric struc tures. All geometric constructions usually are not created equivalent; a few are creations of ~ods whereas others are items of lesser human minds.

This e-book presents a operating wisdom of these elements of external differential varieties, differential geometry, algebraic and differential topology, Lie teams, vector bundles, and Chern types which are worthy for a deeper knowing of either classical and sleek physics and engineering. it's perfect for graduate and complicated undergraduate scholars of physics, engineering or arithmetic as a direction textual content or for self learn.

**Modern geometry. Part 2. The geometry and topology of manifolds**

This can be the 1st quantity of a three-volume creation to trendy geometry, with emphasis on functions to different parts of arithmetic and theoretical physics. issues lined contain tensors and their differential calculus, the calculus of adaptations in a single and several other dimensions, and geometric box thought.

**Advances in Discrete Differential Geometry**

This can be one of many first books on a newly rising box of discrete differential geometry and a very good technique to entry this fascinating region. It surveys the attention-grabbing connections among discrete types in differential geometry and complicated research, integrable platforms and functions in special effects.

- Selected Papers of Kentaro Yano
- Geometric Analysis on the Heisenberg Group and Its Generalizations
- Lectures on the geometry of manifolds
- Method of equivalence and its applications
- Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampere Equations in Two Dimensions

**Additional info for An Invitation to Web Geometry**

**Sample text**

First notice that Eq. u/ ; iD1 then dividing by fk , setting hi D fi =fk and deriving repeatedly with respect to the hamiltonian vector field of u until arriving to an equation depending only on u. 1). k2 1/ then Eq. 1) has to have at least k 1 non-constant solutions vanishing at zero. Consequently k D `. u// D 0. k 1/. t u Webs such as W F of the proposition above, which are obtained from the superposition of a parallel web and one non-linear foliation, will be called quasiparallel webs. 4. C2 ; 0/ !

The real graph of f , which is not differentiable since every point of f is tangent to some leaf of the foliation without being a leaf itself. To summarize: the real trace of a holomorphic (or even polynomial) web can be a non-differentiable, although continuous, foliation (Fig. 9). Fig. Pn ; Symk 1Pn ˝ N / be a k-web on Pn . The degree of W is defined as the number of tangencies, counted with multiplicities, of W with a line not everywhere tangent to W. More precisely, if i W P1 ! P1 ; Symk 1P1 ˝ i N /.

I ^ Ái D 0. Cn ; 0/ ! C; 0/ ! C; 0/. Condition (c) translates into k X gi ı ui D 0 iD1 which is the functional equation among the first integrals of W mentioned at the beginning of the discussion. Cn ; 0/k . It is said to be non-trivial if at least one of the Ái ’s is not identically zero. If none of the 1-forms Ái is identically zero, then the abelian relation P k iD1 Ái D 0 is called complete. W/ Á 0 ” W has a non-trivial abelian relation: To some extent, the main results presented in this book can be seen as generalizations of this equivalence to arbitrary webs of codimension one.