definite metric
11Cartan-Karlhede algorithm — One of the most fundamental problems of Riemannian geometry is this: given two Riemannian manifolds of the same dimension, how can one tell if they are locally isometric? This question was addressed by Elwin Christoffel, and completely solved by… …
12Curvature invariant (general relativity) — Curvature invariants in general relativity are a set of scalars called curvature invariants that arise in general relativity. They are formed from the Riemann, Weyl and Ricci tensors which represent curvature and possibly operations on them such… …
13Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …
14Indefinite inner product space — In mathematics, in the field of functional analysis, an indefinite inner product space :(K, langle cdot,,cdot angle, J) is an infinite dimensional complex vector space K equipped with both an indefinite inner product :langle cdot,,cdot angle and… …
15Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
16Pseudo-Riemannian manifold — In differential geometry, a pseudo Riemannian manifold (also called a semi Riemannian manifold) is a generalization of a Riemannian manifold. It is one of many things named after Bernhard Riemann. The key difference between the two is that on a… …
17Hermitian manifold — In mathematics, a Hermitian manifold is the complex analog of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define …
18nature, philosophy of — Introduction the discipline that investigates substantive issues regarding the actual features of nature as a reality. The discussion here is divided into two parts: the philosophy of physics and the philosophy of biology. In this… …
19Units of measurement — Weights and measures redirects here. For other uses, see Weights and measures (disambiguation). The former Weights and Measures office in Seven Sisters, London A unit of measurement is a definite magnitude of a physical quantity, defined and… …
20Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …
