Existence results of \(\text {Spin}(2, n - 1)_0\)-pseudo-Riemannian cobordisms

In this note, we study necessary and sufficient conditions for the existence of a Spin \((n + 1)\) $(n+1)$ -dimensional cobordism that supports a non-singular and non-degenerate pseudo-Riemannian metric of signature \((2, n - 1)\) $(2,n-1)$ , which restricts to a non-singular time-orientable Lorentzian metric on its boundary. The corresponding cobordism groups are computed.