# Riemannian manifold

> English word · Noun

## Definitions
1. A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
2. A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
(more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.

## Etymology
Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/riemannian-manifold