Killing tensors in two‐dimensional space‐times with applications to cosmology

The existence of Killing vectors and Killing tensors in two‐dimensional space‐times is discussed. The corresponding mechanical problem having a potential with two exponential terms is analyzed in detail and a number of cases admitting Killing tensors are given. The Killing tensors give rise to new exact solutions in perfect fluid Bianchi and Kantowski–Sachs cosmologies as well as in inflationary models with a scalar field source.