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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold〔, p. 172.〕〔, p. 208〕 (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite. Instead a weaker condition of nondegeneracy is imposed on the metric tensor.
Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean space described by an isotropic quadratic form.
A special case of great importance to general relativity is a Lorentzian manifold, in which one dimension has a sign opposite to that of the rest. This allows tangent vectors to be classified into timelike, null, and spacelike. Spacetime can be modeled as a 4-dimensional Lorentzian manifold.
== Introduction ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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