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This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in particular, local notions of angle, length of curves, surface area and volume.
This is a list of differential geometry topics. ... Frenet–Serret formulas; ... List of formulas in Riemannian geometry;
In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics; i.e. a choice of positive-definite quadratic form on a manifold's tangent spaces which varies smoothly from point to point. This gives in particular local ideas of angle, length of curves, and volume.
This is a list of notable theorems. Lists of theorems and similar statements include: ... (Riemannian geometry) A ... Bass-Guirvarc'h formula (group theory) Bass ...
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas [1]) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.
This article includes a list of general references, ... The generalization of the dot product formula to Riemannian manifolds is a defining property of a Riemannian ...
Riemann–Siegel formula; Riemann–Siegel theta function; Riemann–Silberstein vector; Riemann–Stieltjes integral; Riemann–von Mangoldt formula; Riemann's differential equation; Riemann's minimal surface; Riemannian connection on a surface; Riemannian geometry