On the curvatures of \((k+1)\)-dimensional semi-ruled surfaces in \(E_\nu^{n+1}\) (Q1591092)

Given a curve \(\alpha(t)=(\alpha_1(t),\dots,\alpha_{n+1}(t))\) in an \((n+1)\)-dimensional semi-Euclidean space \(E\). Let \(E_{k,\mu}\) denote a \(k\)-dimensional subspace of \(E\), generated by \(\{e_1(t),\dots,e_k(t)\}\), where \(\mu\) is its index. As \(E_{k,\mu}\) moves along a curve \(\alpha\) in \(E\), it forms a \((k+1)\)-dimensional surface, say \(S\). The authors call \(S\) a generalized semi-ruled surface in \(E\). In this paper the authors compute the mean curvature, Riemann curvature, Ricci and scalar curvature of \(S\).