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This is a list of differential geometry topics. ... Laplacian operators in differential geometry; Formulas and other tools. List of coordinate charts;
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science ).
In mathematics, a differential operator is a linear operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another (in the style of a higher-order function in computer science ).
This is a list of formulas encountered in Riemannian geometry. ... is just its usual differential: ... the expression for several operators is simpler.
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra.
The linear operator which assigns to each function its derivative is an example of a differential operator on a function space. By means of the Fourier transform, pseudo-differential operators can be defined which allow for fractional calculus. Some of these operators are so important that they have their own names:
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. It is named after Pierre-Simon Laplace and Eugenio Beltrami.
The Hodge Laplacian, also known as the Laplace–de Rham operator, is a differential operator acting on differential forms. (Abstractly, it is a second order operator on each exterior power of the cotangent bundle.) This operator is defined on any manifold equipped with a Riemannian- or pseudo-Riemannian metric.