Does the concept of differential manifold with negative dimension make sense, in differential geometry?

If yes, how is it defined? Do you have any reference to recommend?

My problem was born in Einstein warped-product manifolds, i.e. to admit a type of metric, the fiber-manifold must have a negative dimension, but I do not know if that manifold makes sense in differential geometry, General Relativity or String Theory…

Thank you for any help