Can the Laplacian of a Scalar Field be Considered as its Curvature?

Swapnil
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Can the laplacian of a scalar field be throught of as its curvature (either approximately or exactly)?
 
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Anyone? Come on! Someone has got to know the answer to my question.:rolleyes:
 
I think the best short answer is "not in general". In some circumstances, however, the Laplacian does arise as a Gaussian curvature for certain manifolds admitting certain kinds of charts. Are you perchance studying the Ricci or Calabi flows?
 

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