Examples of 'covariant derivative' in a sentence
Meaning of "covariant derivative"
covariant derivative - In mathematics, specifically in differential geometry, a covariant derivative is a way of specifying a derivative along a curve or in a vector space that accounts for changes to the basis of the vector space. It is commonly used in the study of connections on differentiable manifolds
How to use "covariant derivative" in a sentence
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covariant derivative
The concept of acceleration is a covariant derivative concept.
And the covariant derivative defined as.
Where the semicolon indicates a covariant derivative.
The covariant derivative giving rise to the gauge group.
Of particular note is their concept of a dynamical covariant derivative.
The covariant derivative.
The curvature tensor measures noncommutativity of the covariant derivative.
Sometimes the covariant derivative along a curve is called absolute or intrinsic derivative.
We also show that the existence of connections implies the existence of covariant derivative.
The covariant derivative of a tensor field is presented as an extension of the same concept.
The Riemann curvature tensor can be expressed in terms of the covariant derivative.
The definition of the covariant derivative does not use the metric in space.
Even to formulate such equations requires a fresh notion, the covariant derivative.
The covariant derivative is a generalization of the directional derivative from vector calculus.
Where D is the exterior covariant derivative.
See also
The gauge covariant derivative is a variation of the covariant derivative used in general relativity.
To answer that question, we will study the connection and covariant derivative.
The exterior covariant derivative extends the exterior derivative to vector valued forms.
In the final webinar of this series, we will explain the covariant derivative.
The covariant derivative is convenient however because it commutes with raising and lowering indices.
Instead of building the directional derivative using partial derivatives, we use the covariant derivative.
They characterize the covariant derivative to be applied to any tensor,.
In curved space-time, we must take the covariant derivative.
Then decompose the ambient covariant derivative of ξ along X into tangential and normal components,.
Specifically, Aμ is found by taking the directional covariant derivative of X along T twice,.
The covariant derivative satisfies,.
However, a given metric uniquely defines a special covariant derivative called the Levi-Civita connection.
The covariant derivative of a type ( r, s ) tensor field along ec is given by the expression,.
These can be defined directly from the induced covariant derivative ∇ on TM as follows.
Sometimes formula 11 is used to represent the four-dimensional Levi-Civita covariant derivative.
See also, Covariant derivative.
If formula 15 vanishes, the curve is called a geodesic of the covariant derivative.
Sometimes ◻ { \ displaystyle \ Box } is used to represent the four-dimensional Levi-Civita covariant derivative.
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