Shoshichi Kobayashi Memorial Volume, Issue 2No Access

Linearization and Gronwall conjecture of Legendrian webs

Tetsuya Ozawa

Department of Mathematics, Meijo University, Nagoya 468-8502, Japan

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and

Hajime Sato

Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

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https://doi.org/10.1142/S0129167X15410037Cited by:0 (Source: Crossref)

Abstract

The Gronwall conjecture, which is still open, asserts that if a 3-web in the plane is linearizable, then the linearization is unique modulo projective transformations. We prove the conjecture for Legendrian d-webs, provided d ≥ 4. Precisely, our theorem states that, if a Legendrian d-web with d ≥ 4 in the (real or complex) 3-dimensional contact manifold is linearizable, then there is a unique linearization of the Legendrian d-web up to a contact projective transformation. For the proof, we use the linearization technique of the third order ordinary differential equations and the Schwarzian derivatives of contact transformations.

In Memory of Professor Shoshichi Kobayashi

Keywords:

AMSC: 53A60, 53D10, 34A26

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