This abbreviated tensor notation is called summation convention and the variable i is called a dummy variable.
3.
Using these properties, the Navier Stokes equations of motion, expressed in tensor notation, are ( for an incompressible Newtonian fluid ):
4.
Which are similar to the Maxwell equations ( when written in tensor notation ), more specifically the Yang Mills equations for quarks and gluons.
5.
Sorry, I am not well acquainted with tensor notation, but in this paper, the author instigates a guage condition to the gravitomagnetic field in equation 10.
6.
The geodesic equation in a radial gravitational field can be described succinctly in tensor notation [ Ref . 2, p . 37 ] in the co-moving frame in which the ceiling of the space craft is in the \ mathbf { \ hat r } direction
7.
"Any physical law which can be expressed in tensor notation in SR has exactly the same form in a locally inertial frame of a curved spacetime . " The 4-gradient commas (, ) in SR are simply changed to covariant derivative semi-colons (; ) in GR, with the connection between the two using Christoffel symbols.
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