A new class of contact pseudo framed manifolds with applications (Q2238443)

On a given manifold \(M\) fix the data \((g, \eta, \xi, f, \lambda)\) with \(g\) a semi-Riemannian metric, \(\eta \) a \(1\)-form, \(\xi \) a vector field which is not null and \(\lambda \) a smooth nonzero function. The author calls \((M, g, \eta, \xi, f, \lambda )\) an almost metric contact pseudo framed (CPF) manifold if \(\eta (\xi )=1\), \(f^3=\lambda ^2f\), \(g(fX, fY)=\mu (g(X, Y)-\varepsilon \sigma ^2\eta (X)\eta (Y))\), \(g(\xi, \xi )=\varepsilon \sigma ^2\), \(g(X, \xi )=\varepsilon \sigma ^2\eta (X)\) where \(\varepsilon =+1\) or \(-1\) if \(\xi \) is space-like or time-like and \(\sigma , \mu \) are other two nonzero smooth functions. Several examples and various types of symmetries, including Ricci solitons, are discussed, some of them inspired by physical models. Two open problems are raised.