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The $AdS$ particle

In this note we have considered a relativistic Nambu-Goto model for a particle in $AdS$ metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed \cite{pal} "Exotic Oscillator". The Snyder algebra and subsequently the $κ$-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncommutative spacetime in the context of open string where only a curved target space is introduced.