Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold

The BRST quantization of particle motion on the hypersurface $V_{(N-1)}$ embedded in Euclidean space $R_N$ is carried out both Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) formalism, second class constrained obtained using analysis are converted into first constraints. Then BFV symmetry constructed. We have given a simple example these kind system. In end we discussed Batalin-Vilkovisky formalism context this (BFFT modified)