Preprints are manuscripts made publicly available before they have been submitted for formal peer review and publication. They might contain new research findings or data. Preprints can be a draft or final version of an author's research but must not have been accepted for publication at the time of submission.
posted on 22.07.2019by Alexey V. Bolsinov, Andrey Yu Konyaev, Vladimir S. Matveev
This work is the first, and main, of the 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.
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
This is an arXiv preprint. It can be found at: https://arxiv.org/abs/1903.04603.