If Hessian Matric H is zero at any point, then the point is called?

If a point is a critical point and its associated Hessian matrix is zero, the point is called a degenerate critical point or a non-Morse critical point. A zero Hessian indicates that the standard second-derivative test, which uses the sign of the Hessian's determinant or eigenvalues to classify extrema, is inconclusive, requiring further analysis to determine if the point is a local maximum, local minimum, or saddle point.