Where \ Lambda _ { R _ 0 } is the RHS ( right hand side ) three-component of volume, log-price differential, and scalar curvature for a rising market.
32.
Lichnerowicz's argument using the Dirac operator has been extended to give many restrictions on non-simply connected manifolds with positive scalar curvature, via the K-theory of C *-algebras.
33.
After work of Schoen, Yau, Gromov, and Lawson, ruled, then " X " ( as a smooth 4-manifold ) has no Riemannian metric with positive scalar curvature.
34.
A constant scalar curvature means a general relativity gravity-like bending of spacetime that has a curvature described by a single number that is the same everywhere in spacetime in the absence of matter or energy.
35.
Briefly, the positive mass conjecture says that if a three-dimensional manifold has positive scalar curvature and is asymptotically flat, then a constant that appears in the asymptotic expansion of the metric is positive.
36.
Where is the determinant of the metric tensor and the Ricci scalar curvature of the 3d geometry ( not including time ), and the " " instead of " " denotes the variational derivative rather than the ordinary derivative.
37.
At first sight, the scalar curvature in dimension at least 3 seems to be a weak invariant with little influence on the global geometry of a manifold, but in fact some deep theorems show the power of scalar curvature.
38.
At first sight, the scalar curvature in dimension at least 3 seems to be a weak invariant with little influence on the global geometry of a manifold, but in fact some deep theorems show the power of scalar curvature.
39.
There, the expansion-recollapse cycle begins and ends with a " strong scalar curvature singularity "; here, we have a mere coordinate singularity ( a circumstance which much confused Einstein and Rosen in 1937 ).
40.
"' Hermann Vermeil "'( 1889 1959 ) was a German mathematician who produced the first published proof that the scalar curvature is the only absolute invariant among those of prescribed type suitable for Einstein s theory.
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