Soliton almost K\"{a}hler structures on 6-dimensional nilmanifolds for the symplectic curvature flow
Abstract
The aim of this paper is to study self-similar solutions to the symplectic cuvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention in the family of symplectic Two- and Three-step nilpotent Lie algebras admitting a "minimal compatible metric" and we give a complete classification of these algebras together with their respective metric. Such classification is given by using our generalization of Nikolayevsky's nice basis criterium (arXiv:1301.4949), which will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds, for the convenience of the reader. By computing the Chern-Ricci operator in each case, we show that the above distinguished metrics define a soliton almost K\"{a}hler structure. Many illustrative examples are carefully developed.
Keywords
Cite
@article{arxiv.1303.5461,
title = {Soliton almost K\"{a}hler structures on 6-dimensional nilmanifolds for the symplectic curvature flow},
author = {Edison Alberto Fernández-Culma},
journal= {arXiv preprint arXiv:1303.5461},
year = {2015}
}
Comments
17 pages, 3 Tables. In this paper, we expand an application given in arXiv:1301.4949 and delete a section given in arXiv:1303.5461v1 on abelian complex structures. A main reference is updated (arXiv:1306.5931 [math.DG]). This is yet a preliminary version; comments, criticisms and suggestions are welcome