Some results on traceless decomposition of tensors

Mikeš, Josef; Jukl, Marek; Juklová, Lenka

doi:10.1007/s10958-011-0321-y

Cited by 17 publications

(8 citation statements)

References 5 publications

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“…In particular, if T (1,2) , T (1,3) , T (1,4) , T (2,3) , T (2,4) , T (3,4) are symmetric, then we have Corollary 1.4. Let V be a real n−dimensional vector space with a metric (inner product)…”

Section: Introductionmentioning

confidence: 94%

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Minimal Norm Tensors Principle and its Applications

Guo¹,

Guan²

2021

Preprint

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In this paper we study the minimal norm tensors for general third covariant tensors and fourth covariant tensors, using this we can give a new explanation of Weyl tensor and Cotten tensor: Weyl tensor is the minimal norm tensor of Riemannian curvature tensor and Cotten tensor is the minimal norm tensor of divergence of Riemannian curvature tensor, and we also get some useful inequalities by computation the norm of minimal norm tensors.

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Section: Introductionmentioning

confidence: 94%

“…Moreover, we denote that 2) , E 2 = (T (1,2) ) T , E 3 = T (1,3) , E 4 = (T (1,3) ) T , E 5 = T (1,4) , E 6 = (T (1,4) ) T…”

Section: Proof Of Main Theoremsmentioning

confidence: 99%

Minimal Norm Tensors Principle and its Applications

Guo¹,

Guan²

2021

Preprint

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“…Formulas (17) and (24) in A n are forming a closed Cauchy-like system of partial differential equation of unknown functionsR h i jk (x) and ϕ i (x). Because theR h i jk (x) are components of the curvature tensor inĀ n , they have to fulfill following identities…”

Section: Canonical F-planar Mappings π(E) E = ±1 Of Space With Affimentioning

confidence: 99%

“…Theorem 4.1. A space A n with affine connection admits the canonical F-planar mapping π(e), e = ±1 onto symmetric spaceĀ n if and only if in A n exists a solution of the mixed Cauchy-like system of the equations (17), (24) and 25, respective the unknown functionsR h i jk (x) and ϕ i (x).…”

Section: R Hmentioning

confidence: 99%

On canonical F-planar mappings of spaces with affine connection

Berezovski

Mikeš

Peška

et al. 2019

Filomat

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In this paper we study the theory of F-planar mappings of spaces with affine connection. We obtained condition, which preserved the curvature tensor. We also studied canonical F-planar mappings of space with affine connection onto symmetric spaces. In this case, the main equations have the partial differential Cauchy type form in covariant derivatives. We got the set of substantial real parameters on which depends the general solution of that PDE's system.

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“…Recently, the golden structure has been studied in [6,7,14,15,22,24,25,26,28,29,32]. In addition to these, some types of polynomial structures was intensively studied in last time, namely an almost product, almost complex, almost tangent and f −structure in [9,10,11,17,18,19].…”

Section: Introductionmentioning

confidence: 99%