# Expression of the restriction of the Laplace-Beltrami operator to a submanifold

Hello everybody, Given the expression of the Laplace-Beltrami operator $\Delta_M$ on a Riemannian manifold $M$, is there any method for determining the expression of the Laplace-Beltrami operator $\Delta_N$ where $N$ is a submanifold of $M$. Actually I am interested in $N=S(Y,r)=$$X\in M s.t. d(X,Y)=r$$$ where $Y\in M$ and $r$ is constant. Thank you Riadh

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