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Nijenhuis geometry

journal contribution
posted on 16.03.2021, 14:28 by Alexey BolsinovAlexey Bolsinov, Andrey Konyaev, Vladimir Matveev
This work is the first, and main, of a series of papers in progress dedicated to Nienhuis operators, i.e., fields of endomorphisms with vanishing Nijenhuis tensor. It serves as an introduction to Nijenhuis Geometry that should be understood in much wider context than before: from local description at generic points to singularities and global analysis. The goal of the present paper is to introduce terminology, develop new important techniques (e.g., analytic functions of Nijenhuis operators, splitting theorem and linearisation), summarise and generalise basic facts (some of which are already known but we give new self-contained proofs), and more importantly, to demonstrate that the research programme proposed in the paper is realistic by proving a series of new, not at all obvious, results.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Advances in Mathematics

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Advances in Mathematics and the definitive published version is available at https://doi.org/10.1016/j.aim.2021.108001.

Acceptance date

27/01/2021

Publication date

2021-09-28

Copyright date

2021

ISSN

0001-8708

Language

en

Depositor

Dr Alexey Bolsinov. Deposit date: 14 March 2021

Article number

108001

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