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# Tensor

## Category Documents

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DifferentialGeometry/Tensor/AdaptedNullTetrad

find a null tetrad which transforms the Newman-Penrose Weyl scalars to a standard form

find a null tetrad which transforms the Newman-Penrose Weyl scalars to a standard form

DifferentialGeometry/Tensor/AdaptedSpinorDyad

find a spinor dyad which transforms the Weyl spinor to normal form

find a spinor dyad which transforms the Weyl spinor to normal form

DifferentialGeometry/Tensor/CheckKillingTensor

check that a tensor is the Killing tensor for a given metric or connection

check that a tensor is the Killing tensor for a given metric or connection

DifferentialGeometry/Tensor/Christoffel

find the Christoffel symbols of the first or second kind for a metric tensor

find the Christoffel symbols of the first or second kind for a metric tensor

DifferentialGeometry/Tensor/ConformalKillingVectors

calculate the conformal Killing vectors for a given metric

calculate the conformal Killing vectors for a given metric

DifferentialGeometry/Tensor/Connection

define a linear connection on the tangent bundle or on a vector bundle

define a linear connection on the tangent bundle or on a vector bundle

DifferentialGeometry/Tensor/CovariantDerivative

calculate the covariant derivative of a tensor field with respect to a connection

calculate the covariant derivative of a tensor field with respect to a connection

DifferentialGeometry/Tensor/CovariantlyConstantTensors

calculate the covariantly constant tensors with respect to a given metric or connection

calculate the covariantly constant tensors with respect to a given metric or connection

DifferentialGeometry/Tensor/CurvatureTensor

calculate the curvature tensor of a linear connection on the tangent bundle or on a vector bundle

calculate the curvature tensor of a linear connection on the tangent bundle or on a vector bundle

DifferentialGeometry/Tensor/DirectionalCovariantDerivative

calculate the covariant derivative of a tensor field in the direction of a vector field and with respect to a given connection

calculate the covariant derivative of a tensor field in the direction of a vector field and with respect to a given connection

DifferentialGeometry/Tensor/FormInnerProduct

compute the inner product of two forms with respect to a given metric tensor

compute the inner product of two forms with respect to a given metric tensor

DifferentialGeometry/Tensor/GenerateSymmetricTensors

generate a list of symmetric tensors from a list of tensors

generate a list of symmetric tensors from a list of tensors

DifferentialGeometry/Tensor/GenerateTensors

generate a list of all product tensors from a list of lists of tensors

generate a list of all product tensors from a list of lists of tensors

DifferentialGeometry/Tensor/GeodesicEquations

calculate the geodesic equations for a symmetric linear connection on the tangent bundle

calculate the geodesic equations for a symmetric linear connection on the tangent bundle

DifferentialGeometry/Tensor/IndependentKillingTensors

given two lists R and S of rank p Killing tensors, find a maximal sublist T of R such that the combined list of tensors [T, S] are linearly independent (over the real numbers)

given two lists R and S of rank p Killing tensors, find a maximal sublist T of R such that the combined list of tensors [T, S] are linearly independent (over the real numbers)

DifferentialGeometry/Tensor/InfinitesimalHolonomy

find the matrix Lie algebra giving the infinitesimal holonomy of a metric or a connection on the tangent bundle or on a general vector bundle

find the matrix Lie algebra giving the infinitesimal holonomy of a metric or a connection on the tangent bundle or on a general vector bundle

DifferentialGeometry/Tensor/InvariantTensorsAtAPoint

find tensors or differential forms which are invariant under the infinitesimal action of a set of matrices

find tensors or differential forms which are invariant under the infinitesimal action of a set of matrices

DifferentialGeometry/Tensor/KillingBracket

a covariant form of the Schouten bracket for symmetric tensors

a covariant form of the Schouten bracket for symmetric tensors

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