I work in holography and I'm trying to get my feet when in non-relativistic holography. Can someone explain exactly what an "isometry" is in this context?
"the correspondence can be extended to a non-relativistic holography by taking background geometries in General Relativity that have non-relativistic isometries like Schrödinger or Lifshitz symmetries, which are the typical symmetries of a wide class of field theories describing non-relativistic phenomena."
My knowledge is this: in group theory, two groups are homomorphic, in topology, two spaces are homeomorphic, and in geometry, two geometries are isometric. My topology instructor said this once, but I have no formal geometry instruction outside of a GR course and so don't fully understand it.