Canonical basic \(f\)-structures and some classes of structures in generalized Hermitian geometry (Q2799776)

A \(\Phi\)-space of order \(k\) is a homogeneous \(k\)-symmetric space \(G/H\) of a connected Lie group \(G\) with an automorphism \(\Phi\) satisfying \(\Phi^k=\mathrm{id}\). An \(f\)-structure is a \((1,1)\)-tensor \(f\) on a manifold \(M\) satisfying a certain simple polynomial identity. In the case of a (pseudo-)Riemannian manifold \((M,\langle.,.\rangle)\) \(f\) is called a metric \(f\)-structure if \(\langle fX,Y\rangle+\langle X,fY\rangle\) for all vector fields \(X,Y\) on \(M\). Certain classes of invariant \(f\)-structures on \(\Phi\)-spaces, among them nearly Kählerian, \(G_1f\)-structures, Hermitian, Kählerian, quasi-Kählerian and Killing \(f\)-structures defined and have been studied in a number of earlier papers. Here, the author presents classification results on \(\Phi\)-spaces with fundamental \(f\)-structures recently found, as well as new ones.NEWLINENEWLINEFor the entire collection see [Zbl 1298.53003].