Matter Fields in Curved Space-Time
  We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions. 
Nguyen Ai Viet and Kameshwar C. Wali