Isometry Group of Superfluids

A space-time with geometry determined by superfluid energy-momentum tensor is considered. Groups of isometry are investigated under the assumption that movements of superfluid and normal components are directed along different Killing vector fields. It is shown that operators generated by the Killing vectors associated with the superfluid and normal flow constitute the center of Lie algebra. All possible groups of isometry satisfying this condition are specified and investigated. A unique gravitational field is shown to exist, admitting the isometry group of order $r\ge4$.