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Let [itex]g_{ij}[/itex] be a tensor, where [itex]0 \leq i,j \leq n[/itex]. The Morse index [itex]\mu[/itex] is the number of negative eigenvalues of g. On page 469 of Eberhard Zeidler's QFT III: Gauge Theory, it says that g is Riemannian if [itex]\mu = 0[/itex] and pseudo-Riemannian if [itex]0 < \mu < n[/itex]. Is this correct? If so, what kind of tensor is it when [itex]\mu = n[/itex]?