Examples of 'curvature tensor' in a sentence
Meaning of "curvature tensor"
curvature tensor - In mathematics and physics, a curvature tensor is a mathematical object that describes how a geometric quantity such as a curve or surface deviates from being a straight line or flat. It is used in the study of differential geometry and general relativity to understand the curvature of spacetime
How to use "curvature tensor" in a sentence
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curvature tensor
The curvature tensor measures noncommutativity of the covariant derivative.
The sectional curvature determines the curvature tensor completely.
The Riemann curvature tensor can be expressed in terms of the covariant derivative.
One example is the Riemann curvature tensor.
The Riemann curvature tensor directly measures the failure of this in a general Riemannian manifold.
This difference is measured by the Riemann curvature tensor.
Riemann curvature tensor.
The fundamental object is called the Riemann curvature tensor.
Einstein curvature tensor.
It is obtained by averaging certain portions of the Riemann curvature tensor.
There are a few books where the curvature tensor is defined with opposite sign.
From this tensor one can compute the Riemann curvature tensor.
This is simply the Riemann curvature tensor in a different form.
The Gravitational field is identified by the Riemann curvature tensor.
The curvature tensor doesn't vanish anywhere on a sphere.
See also
Note that the Ricci tensor can be zero without the Curvature tensor being it.
Occasionally, the curvature tensor is defined with the opposite sign.
Those not using an index notation usually reserve R for the full Riemann curvature tensor.
Where the Ricci curvature tensor.
Some well known examples of tensors in geometry are quadratic forms, and the curvature tensor.
In terms of the Riemann curvature tensor and the Christoffel symbols, one has.
Starting with dimension 3, scalar curvature does not describe the curvature tensor completely.
In Euclidean space, the curvature tensor of a submanifold can be described by the following formula,.
In this co-moving coordinate system the curvature tensor is diagonal.
A curvature tensor 3 . An abbreviation for right moving modes.
With four or more dimensions, Ricci curvature does not describe the curvature tensor completely.
In dimensions 2 and 3 the Weyl curvature tensor vanishes identically.
Minkowski space and Maxwell 's equations in vacuum can be embedded in a five-dimensional Riemann curvature tensor.
The Space-time is called " flat " when the curvature tensor is zero.
Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor.
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Examples of using Curvature
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The distinct curvature of the femur is undeniable
Differences between the radii of curvature of mirrors
Her curvature of the spine is hardly noticeable
Examples of using Tensor
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The metric tensor is an example of a tensor field
This is similar to the notion of tensor rank
The zero tensor has rank zero
