Weyl-Einstein structures on K-contact manifolds (Q2406829)

The main result of the work is an important theorem. Theorem. Let \((M^{2m+1},g,\xi)\), \(m\geq 1\), be a compact K-contact manifold carrying a closed Weyl-Einstein structure \(D\) compatible with the conformal class \(c=[g]\). Then \(D\) is the Levi-Cività connection of \(g\) which is then Einstein. From this theorem it follows that if j\((M^{2m+1},g,\xi)\) is a compact K-contact manifold carrying a closed Weyl-Einstein structure compatible with \(g\), then \(M^{2m+1}\) is Sasaki-Einstein.