bianchi identity造句

• The Bianchi identity associated with this partial gauge invariance is wrong.
• Of particular relevance to general relativity are the algebraic and differential Bianchi identities.
• However, in order to define the Hodge star, the Laplacian, the first Bianchi identity and the Yang-Mills functional, one needs the bundle metric.
• This means that 2-brane and 5-brane charge are the violations of the Bianchi identities for the dual C-field and original C-field respectively.
• The last identity was discovered by Ricci, but is often called the " first Bianchi identity ", just because it looks similar to the Bianchi identity below.
• The last identity was discovered by Ricci, but is often called the " first Bianchi identity ", just because it looks similar to the Bianchi identity below.
• As is the case with magnetic monopoles in electromagnetism, this source also invaliditates the dual Bianchi identity as it is a point at which the dual field is not defined.
• They will obey the usual symmetry properties; for example, the curvature of the connection will be anti-symmetric in the last two indexes, and will satisfy the second Bianchi identity.
• The Bianchi identities of the Ramond-Ramond gauge potentials C _ { 2k-1 } can be violated by adding sources \ rho, which are called D ( 8 & minus; 2 " k " )-branes
• The above Bianchi identity is interpreted to mean that the Dp-brane is, in analogy with magnetic monopoles in electromagnetism, magnetically charged under the RR " p "-form " C " 7 & minus; " p ".
• From the above Bianchi identity we see that a D8-brane is a domain wall between zones of differing " G " 0, thus in the presence of a D8-brane at least part of the spacetime will be described by the Romans theory.
• Conversely, except in dimension 2, if the curvature of a Riemannian manifold has this form for some function " K ", then the Bianchi identities imply that " K " is constant and thus that the manifold is ( locally ) a space form.
• Variation of the first term of the action with respect to the tetrad e ^ { \ alpha } _ { \ I } gives the ( mixed index ) Einstein tensor and variation of the second term with respect to the tetrad gives a quantity that vanishes by symmetries of the Riemann tensor ( specifically the first Bianchi identity ), together these imply Einstein's vacuum field equations hold.
• In 1902, Bianchi rediscovered what are now called the Bianchi identities for the Riemann tensor, which play an even more important role in general relativity . ( They are essential for understanding the Einstein field equation . ) According to Tullio Levi-Civita, these identities had first been discovered by Ricci in about 1880, but Ricci apparently forgot all about the matter, which led to Bianchi's rediscovery.