Non-Euclidean geometry and Riemannian geometry

Non-Euclidean geometry noun - (mathematics) geometry based on axioms different from Euclid's.

Riemannian geometry and non-Euclidean geometry are semantically related. In some cases you can replace phrase "Riemannian geometry" with "Non-Euclidean geometry", this phrases are similar.

Riemannian geometry noun - (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle.

Non-Euclidean geometry and Riemannian geometry are semantically related. You can use "Non-Euclidean geometry" instead a noun phrase "Riemannian geometry".