The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime.

Prominent in these geometrical lunar theories were combinations of circular motions - applications of the theory of epicycles.

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915/16.

The diffeomorphism group is by definition a local symmetry and thus every geometrical or generally covariant theory (i.e. a theory whose equations are tensor equations, for example general relativity) has local symmetries.

UTD is an extension of Joseph Keller's geometrical theory of diffraction (GTD).

It was argued that Cubism itself was not based on any geometrical theory, but that non-Euclidean geometry corresponded better than classical, or Euclidean geometry, to what the Cubsists were doing.

Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere.

The solution in cylindrical coordinates was then extended to the optical regime by Joseph B. Keller, who introduced the notion of diffraction coefficients through his geometrical theory of diffraction (GTD).

Cubism itself, then, was not based on any geometrical theory, but corresponded better to non-Euclidean geometry than classical or Euclidean geometry.

While the two above variants are explicable in simple terms based on geometrical theory (basically, the Bragg law) or kinematical theory of X-ray diffraction, extinction contrast can be understood based on dynamical theory.