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 in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) method, the second class constraints obtained using Hamiltonian analysis are converted into first class constraints. Then using BFV analysis the BRST symmetry is constructed. We have given a simple example of these kind of system. In the end we have discussed Batalin-Vilkovisky formalism in the context of this (BFFT modified) system.