Manifolds of constant negative curvature as vacuum solutions in Kaluza–Klein and superstring theories

New solutions are found for the equations of Kaluza–Klein theory and superstrings corresponding to spontaneous compactification and using compact manifolds of constant negative curvature and surfaces of KЗ type. The part played by manifolds of constant negative curvature in Kaluza–Klein theory is discussed. Solutions corresponding to the existence of additional time dimensions with vanishing cosmological constant are also found.