On real hypersurfaces in a quaternionic hyperbolic space in terms of the derivative of the second fundamental tensor (Q1872914)

For a real hypersurface \(M\) in quaternionic space \(QH^m, m\geq 2\), the second fundamental form \(H\) may satisfy the condition \[ (\nabla_XH)Y=\sum\{\eta_i(Y)\phi_iX+g(\phi_iX, Y)U_i\} \] for any tangent vector fields \(X\) and \(Y\) of \(M\), where \(\phi_iX\) is the tangent component of \(J_iX\) in local basis of quaternionic structure and \(\eta_i(Y)=g(Y,\xi_i)\), \(i=1,2,3\). The connection \(\nabla\) of \(M\) is induced from \(QH^m\) (type \(A_0\)) or a tube of radius \(r\) over totally geodesic \(QH^k\) for \(k\in\{0,1,\ldots, n-1\}\) (type \(A\)).