Soliton almost K\"{a}hler structures on 6-dimensional nilmanifolds for the symplectic curvature flow

Edison Alberto Fernández-Culma

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arXiv · 1303.5461

Soliton almost K\"{a}hler structures on 6-dimensional nilmanifolds for the symplectic curvature flow

Edison Alberto Fernández-Culma

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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 $P$ in each case, we show that the above distinguished metrics define a soliton almost K\"{a}hler structure. Many illustrative examples are carefully developed.

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BibTeX RIS

Edison Alberto Fernández-Culma. 2013-03-21. Soliton almost K\"{a}hler structures on 6-dimensional nilmanifolds for the symplectic curvature flow. https://arxiv.org/abs/1303.5461

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