Classification of second orders symmetric tensors on manifolds through an associated fourth order tensor
Filomat, Tome 37 (2023) no. 25, p. 8489

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For a manifold M admitting a metric g and given a second order symmetric tensor T on M one can construct from g and (the trace-free part of) T a fourth order tensor E on M which is related in a one-to-one way with T and from which T may be readily obtained algebraically. In the case when dimM = 4 this leads to an interesting relationship between the Jordan-Segre algebraic classification of T, viewed as a linear map on the tangent space to M with respect to g, and the Jordan-Segre classification of E, viewed as a linear map on the 6−dimensional vector space of 2−forms to itself (with respect to the usual metric on 2−forms). This paper explores this relationship for each of the three possible signatures for g.
DOI : 10.2298/FIL2325489H
Classification : 53C21
Keywords: Tensor classification, Neutral signature
Graham Hall. Classification of second orders symmetric tensors on manifolds through an associated fourth order tensor. Filomat, Tome 37 (2023) no. 25, p. 8489 . doi: 10.2298/FIL2325489H
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     title = {Classification of second orders symmetric tensors on manifolds through an associated fourth order tensor},
     journal = {Filomat},
     pages = {8489 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325489H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325489H/}
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