In Euclidean space, where is the Kronecker delta (which is 0 for and 1 for ), reproducing the usual form of the Pythagorean theorem (2) In this way, the metric tensor can be thought of as a tool by which geometrical characteristics of a space can be "arithmetized" by way of intr...
$g_a^b$ is just notational sugar for $g_{ac} g^{bc}$, and the fact that the components of this are equal to the Kronecker delta tensor is exactly because $g^{ab}$ is the inverse of $g_{ab}$, in the sense described in point 1. (My answer probably does not add much beyond...
We can use the fact that the metric contracted with its inverse gives a Kronecker delta ηαμημτ=δταηαμημτ=δατ and multiply both sides by ηαμηαμ. We don't wantare not allowed to contract both indices μ,τμ,τ of ηη, as you attempted, because when one ...
The equations (1) lead to the “nonconservation” of matter energy-momentum tensor which makes more sophisticate the physical interpretation of such models and solutions of dynamical or evolution equations. Nevertheless, we can elaborate on a nonholonomic deformation formalism with adapted distortions ...
For example, the Kaplunovsky-Louis soft terms in gravity mediated supersymmetry breaking [11] involve curvature tensors in field space. In general, we would like to know the moduli space metric GT T¯, including quantum corrections. In minimal supersymmetry, the moduli space metric GT T¯...
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Open Access Policy Institutional Open Access Program Special Issues Guidelines Editorial Process Research and Publication Ethics Article Processing Charges Awards Testimonials Author Services Initiatives Sciforum MDPI Books Preprints.org Scilit SciProfiles Encyclopedia JAMS Proceedings Series About Overview ...