Basically, any nonzero component of the stress-energy tensor causes a curvature in spacetime, to use the general relativity description, and thermal energy is in general only a minor contributor to the stress-energy tensor, so zero thermal energy does not at all imply a zero curvature of spacetime.
22.
In spaces with a positive-definite quadratic form ( i . e . Euclidean space ), the quasi-spheres with negative radius squared are the empty set, those with zero radius each consist of a single point, those with positive radius squared are standard-spheres, and those with zero curvature are hyperplanes.
23.
One-dimensional cases include autowave spread in cable and its spread in the ring, with the latter mode considering as a limiting case of a rotating wave in two-dimensional active medium, while the first case is considered as spread of the autowave in the ring with zero curvature ( i . e ., with an infinite radius ).
24.
In this expression, \ Delta p = p _ { l }-p _ { v } is the pressure difference between the ( bulk ) pressure of the liquid inside and the pressure of the vapour outside, and \ sigma is the surface tension of the " planar interface ", i . e . the interface with zero curvature R = \ infty.
25.
Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions every surface admits a constant curvature metric; geometrically, it has one of 3 possible geometries : positive curvature / spherical, zero curvature / flat, negative curvature / hyperbolic and the geometrization conjecture ( now theorem ) in 3 dimensions every 3-manifold can be cut into pieces, each of which has one of eight possible geometries.
26.
Low-dimensional topology is strongly geometric, as reflected in the uniformization theorem in 2 dimensions every surface admits a constant curvature metric; geometrically, it has one of 3 possible geometries : positive curvature / spherical, zero curvature / flat, negative curvature / hyperbolic and the geometrization conjecture ( now theorem ) in 3 dimensions every 3-manifold can be cut into pieces, each of which has one of 8 possible geometries.
