A self-adjoint elliptic differential operator defined somewhat technically as
 |
where 
is the exterior derivative and 
and 
are adjoint to each other with respect to the inner
product.
Laplace-Beltrami Operator
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 628, 1980.Referenced on Wolfram|Alpha
Laplace-Beltrami OperatorCite this as:
Weisstein, Eric W. "Laplace-Beltrami Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Laplace-BeltramiOperator.html