Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A Riemannian product is a product manifold equipped with the product metric from its factors.
|
| gptkbp:example |
The product of two spheres with their standard metrics is a Riemannian product.
|
| gptkbp:field |
differential geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemannian product
|
| gptkbp:introduced |
gptkb:Élie_Cartan
|
| gptkbp:property |
The metric on the product is the sum of the metrics on the factors.
Geodesics in the product are products of geodesics in the factors. |
| gptkbp:relatedTo |
gptkb:Riemannian_manifold
product manifold |
| gptkbp:usedIn |
gptkb:Riemannian_geometry
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|