Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow

EDISON ALBERTO FERNÁNDEZ CULMA

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2015 vol. 25 p. 2736 - 2758

1050-6926

The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent Lie algebras admitting a minimal compatible metric and give a complete classification of these algebras together with their respective metric. Such a classification is given by using our generalization of Nikolayevsky´s nice basis criterion, which, for the convenience of the reader, will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds. 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.