sectional curvature

Let M be a Riemannian manifoldMathworldPlanetmath. Let p be a point in M and let S be a two-dimensional subspace of TpM. Then the sectional curvatureMathworldPlanetmath of S at p is defined as


where x,y span S, g is the metric tensor and R is the Riemann’s curvature tensor.

This is a natural generalization of the classical Gaussian curvatureMathworldPlanetmath for surfaces.

Title sectional curvature
Canonical name SectionalCurvature
Date of creation 2013-03-22 15:54:15
Last modified on 2013-03-22 15:54:15
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 5
Author juanman (12619)
Entry type Definition
Classification msc 53B21
Classification msc 53B20
Related topic RiemannianMetric