Some aspects of the three dimensional gravity theories with temporal   scalar field
  The present paper proposes a new explanation for the 3-dimensional Einstein general theory of relativity which is free of contradictions and consistent with usual 4-dimensional physics. We discuss the property of the new gravity theory with temporal scalar field arise in lower-dimensional theories as the reduction of timelike extra dimension. These ideas we continued by using the 3-dimensional analog of Jordan, Brans-Dicke theory with temporal scalar field where space and time are treated in different ways. 
S.M.Kozyrev