|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:Metric
gptkb:Tensor
|
|
gptkbp:actsOn
|
tangent space
|
|
gptkbp:codomain
|
real numbers
|
|
gptkbp:component_notation
|
g_ij
|
|
gptkbp:contrastsWith
|
gptkb:pseudo-Riemannian_metric
|
|
gptkbp:defines
|
gptkb:region
Angle
length of curves
|
|
gptkbp:domain
|
gptkb:Riemannian_manifold
|
|
gptkbp:enables
|
measurement of angles
measurement of areas
measurement of lengths
measurement of volumes
|
|
gptkbp:field_of
|
differential geometry
|
|
gptkbp:generalizes
|
Euclidean metric
|
|
gptkbp:heldBy
|
symmetric bilinear form
(0,2)-tensor
positive-definite metric
smooth field
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Riemannian metric tensor
|
|
gptkbp:introduced
|
gptkb:Bernhard_Riemann
|
|
gptkbp:is_a_section_of
|
symmetric 2-tensor bundle
|
|
gptkbp:is_non-degenerate
|
true
|
|
gptkbp:is_positive-definite
|
true
|
|
gptkbp:is_smooth
|
true
|
|
gptkbp:used_in
|
gptkb:general_relativity
gptkb:theoretical_physics
gptkb:topology
gptkb:Riemannian_geometry
global analysis
manifold theory
|
|
gptkbp:used_to_define
|
geodesics
curvature
volume form
|
|
gptkbp:bfsParent
|
gptkb:Riemannian_geometry
gptkb:Riemannian_manifold
|
|
gptkbp:bfsLayer
|
5
|