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This thesis explores a role of space-time folation. One can consider the \((3+1)\)-dimensional space-time as a \(3\)-dimensional space parametrized by time; here, the \(3\)-dimensional space (spatial hypersurface) is called foliation of space-time. Piling up foliations along a time direction, one can “reconstruct” space-time. Due to one of the guiding principles of general relativity, general covariance or diffeomorphism invariance, a shape of the space-time foliation is, in fact, not essential: it is a gauge artifact.