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Tensor field

In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of a physical space, in which case the field quantity acquires a unit of measurement. Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the…

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Overview

Intrinsic approach

In coordinates

Tensor fields as multilinear forms

Applications

Tensor calculus

Twisting by a line bundle

Flat case

Cocycles and chain rules

Generalizations

Advanced semantic analysis

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Map overview Semantic statistics

Tensor field

Nodes98
Edges97
Triples55
Avg. degree1.98
Density0.020408
Components1

How this topic connects Entity context

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Tensor field

Top relations

related to Tensor densities · 9
Tensor field → An, Einstein, Higher, Hilbert, Invariantly, Jacobian, Scalar, The, They
related to Twisting by a line bundle · 8
Tensor field → An, For, If, In, Ls, One, This, To
related to Tensor fields as multilinear forms · 6
Tensor field → As, First, Omega, The, There, These
related to Definition · 5
Tensor field → Equivalently, Euclidean, Let, The, This
related to Flat case · 5
Tensor field → As, Euclidean, The, This, When
is a · 4
Tensor field → assignment of elements T, element of this set, function assigning a tensor to each point of a region of a mathematical space, generalization of a scalar field and a vector field that assigns
related to Cocycles and chain rules · 4
Tensor field → Abstractly, As, It, The
related to Notation · 4
Tensor field → The, This, Thus, TM
related to Tensor calculus · 4
Tensor field → Even, In, The, This
has application · 3
Tensor field → Einstein's, In, The

Important terminology Word statistics

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Important terminology

tensor field displaystyle vector fields bundle space manifold tensors point coordinate one example coordinates functions general densities case isbn density

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tensor fieldis afunction assigning a tensor to each point of a region of a mathematical space0.90text
Tensor fieldis ageneralization of a scalar field and a vector field that assigns0.90text
Tensor fieldis aassignment of elements T0.90text
Tensor fieldis aelement of this set0.90text
defining integral operators on manifoldsinstance ofand consider tensor density fields with weight s.Half-densities are applied in areas0.80text
and geometric quantizationinstance ofand consider tensor density fields with weight s.Half-densities are applied in areas0.80text
theinstance ofone can think of tensor densities as multilinear maps taking their values in a density bundle0.80text
Tensor fieldhas applicationThe0.60section
Tensor fieldhas applicationEinstein's0.60section
Tensor fieldhas applicationIn0.60section
Tensor fieldrelated to Cocycles and chain rulesAs0.60section
Tensor fieldrelated to Cocycles and chain rulesAbstractly0.60section

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