higher curvature
1Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …
2Curvature 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… …
3Higher-dimensional Einstein gravity — is any of various physical theories that attempt to generalise to higher dimensions various results of the well established theory of standard (four dimensional) Einstein gravity, that is, general relativity. This attempt at generalisation has… …
4Ricci curvature — In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci Curbastro, provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n… …
5Total curvature — In mathematical study of the differential geometry of curves, the total curvature of a plane curve is the integral of curvature along a curve taken with respect to arclength::int a^b k(s),ds.The total curvature of a closed curve is always an… …
6Principal curvature — Saddle surface with normal planes in directions of principal curvatures In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface… …
7Constant curvature — See also: Space form In mathematics, constant curvature in differential geometry is a concept most commonly applied to surfaces. For those the scalar curvature is a single number determining the local geometry, and its constancy has the obvious… …
8Prescribed scalar curvature problem — In Riemannian geometry, a branch of mathematics, the prescribed scalar curvature problem is as follows: given a closed, smooth manifold M and a smooth, real valued function f on M , construct a Riemannian metric on M whose scalar curvature equals …
9photoreception — photoreceptive, adj. /foh toh ri sep sheuhn/, n. the physiological perception of light. [1905 10; PHOTO + RECEPTION] * * * Biological responses to stimulation by light, most often referring to the mechanism of vision. In one celled organisms such …
10Pp-wave spacetime — In general relativity, the pp wave spacetimes, or pp waves for short, are an important family of exact solutions of Einstein s field equation. These solutions model radiation moving at the speed of light. This radiation may consist of:*… …
