Weyl space forms and their submanifolds (Q2717745)

There is a unique metric \(g\) in the conformal structure of a compact Weyl manifold \((M,[g],D)\), \(Dg=\omega\otimes g\), with respect to which \(\omega\) is co-closed. Such metric \(g\) is said to be a Gauduchon metric and \((M,g, D)\) is said to be a Gauduchon manifold. In the paper the geometric structure of a Gauduchon manifold of constant curvature is studied. A necessary and sufficient condition for a Gauduchon manifold to be of constant curvature is found. The classification of such manifolds is given. Finally, Weyl submanifolds of the Gauduchon flat manifolds are studied.