Search results
Results from the WOW.Com Content Network
Christoffel symbols satisfy the symmetry relations = or, respectively, =, the second of which is equivalent to the torsion-freeness of the Levi-Civita connection. The contracting relations on the Christoffel symbols are given by
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. [1] The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface.
However, the Levi-Civita symbol is a pseudotensor because under an orthogonal transformation of Jacobian determinant −1, for example, a reflection in an odd number of dimensions, it should acquire a minus sign if it were a tensor. As it does not change at all, the Levi-Civita symbol is, by definition, a pseudotensor.
In one version of the prophet Tiresias's sex-change story which includes a cycle of seven transformations alternating between male and female, in the end Aphrodite, who finally changes him into a woman, gets annoyed at Tiresias over some insult and transforms them into a mouse. Titanis: Doe: Artemis
A nontensor is a tensor-like quantity that behaves like a tensor in the raising and lowering of indices, but that does not transform like a tensor under a coordinate transformation. For example, Christoffel symbols cannot be tensors themselves if the coordinates do not change in a linear way.
The (c. 4th century) encyclopedic Guanzi text uses bianhua 5 times (3 in the Xinshu 心術 "Mind Techniques" chapters). Where the Xingshi 形勢 "Conditions and Circumstances" chapter says "The Way brings about the transformation of the self", the corresponding 形勢解 "Explanation" chapter elucidates "The Way is the means by which the self is transformed so a person will adhere to correct ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Also, as length contraction does not affect the perpendicular dimensions of an object, the following remain the same as in the Galilean transformation: ′ = ′ = Finally, to determine how t and t′ transform, substituting the x↔x′ transformation into its inverse: