Soliton almost Kähler structures on 6-dimensional nilmanifolds for the symplectic curvature flow

2013/03/21 by Fernández-Culma, Edison Alberto
#22E45 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 57N16. Secondary 22E25 #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1303.5461

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 Kähler structure. Many illustrative examples are carefully developed.

Related

• A canonical compatible metric for geometric structures on nilmanifolds
• The Ricci Flow for Nilmanifolds
• On the symplectic curvature flow for locally homogeneous manifolds
• The Existence of Soliton Metrics for Nilpotent Lie Groups
• Geometric structures on nilpotent Lie groups: on their classification and a distinguished compatible metric