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Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

A method of determining coefficients alpha_l in an expansion y(x)=y_0(x)+sum_(l=1)^qalpha_ly_l(x) so as to nullify the values of an ordinary differential equation L[y(x)]=0 ...

Newton's term for a variable in his method of fluxions (differential calculus).

The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...

A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

The space of currents arising from rectifiable sets by integrating a differential form is called the space of two-dimensional rectifiable currents. For C a closed bounded ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...