Existence results of 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.