scalar curvature वाक्य
उदाहरण वाक्य
मोबाइल
- Where \ mathbf { R } is the Ricci tensor, \ mathbf { g } is the metric tensor and R is the scalar curvature.
- He is best known for his work in conformal geometry, his study of extremal metrics and his research on scalar curvature and Q-curvature.
- Kazdan Warner's result focuses attention on the question of which manifolds have a metric with positive scalar curvature, that being equivalent to property ( 1 ).
- Unlike the Riemann curvature tensor or the Ricci tensor, both of which can be defined for any affine connection, the scalar curvature requires a metric of some kind.
- For example, the Ricci tensor is a non-metric contraction of the Riemann curvature tensor, and the scalar curvature is the unique metric contraction of the Ricci tensor.
- In relativity, if translations mix up nontrivially with rotations, but the universe is still homogeneous and isotropic, the only option is that spacetime has a uniform scalar curvature.
- As a consequence, a metric-affine f ( R ) gravity, whose Lagrangian is an arbitrary function of a scalar curvature R of \ Gamma, is considered.
- Where ?" " x " } } is the Riemannian norm in the tangent space at, is the divergence of at, and is the scalar curvature at.
- In 1997, together with Tom Ilmanen ( ETH Zurich ), he was able to prove the Riemannian manifold with positive scalar curvature, in the presence of a single black hole.
- For example, Gromov and Lawson showed that a closed manifold that admits a metric with sectional curvature d " 0, such as a torus, has no metric with positive scalar curvature.
- Where \ Lambda _ { R _ 0 } is the RHS ( right hand side ) three-component of volume, log-price differential, and scalar curvature for a rising market.
- 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.
- After work of Schoen, Yau, Gromov, and Lawson, ruled, then " X " ( as a smooth 4-manifold ) has no Riemannian metric with positive scalar curvature.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 ).
- "' 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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