Schr\"{o}dinger equations in constrained space with several initial   constraints
  A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not only on the coordinates but also on the velocities. It is shown that the hermiticity for the observables of the system restricts the geometrical structure of our world. 
Masanobu Nojiri, Takashi Matsunaga, Tadashi Miyazaki, Chi\'e Ohzeki   and Motowo Yamanobe