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Structural equations for a special class of conformal Killing tensors of arbitrary valence

Michael Crampin (UGent)
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Abstract
A symmetric tensor T on a (pseudo-)Riemannian manifold which satisfies T-i1,(i2),....,(irij) = S((i1),(i2),....,(ir-1)g(ir))j for some symmetric tensor S is a conformal Killing tensor of a special kind. Such special conformal Killing tensors of valence I and 2 have been extensively studied. In this paper special conformal Killing tensors of arbitrary valence, and indeed certain non-metrical generalizations of them, are investigated. In particular, it is shown that the space of special conformal Killing tensors is finite dimensional, and the maximal dimension is attained (in the (pseudo-)Riemannian case) if and only if the manifold is a space of constant curvature. This result is obtained by constructing a set of structural equations for special conformal Killing tensors.

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MLA
Crampin, Michael. “Structural Equations for a Special Class of Conformal Killing Tensors of Arbitrary Valence.” REPORTS ON MATHEMATICAL PHYSICS 62.2 (2008): 241–254. Print.
APA
Crampin, Michael. (2008). Structural equations for a special class of conformal Killing tensors of arbitrary valence. REPORTS ON MATHEMATICAL PHYSICS, 62(2), 241–254.
Chicago author-date
Crampin, Michael. 2008. “Structural Equations for a Special Class of Conformal Killing Tensors of Arbitrary Valence.” Reports on Mathematical Physics 62 (2): 241–254.
Chicago author-date (all authors)
Crampin, Michael. 2008. “Structural Equations for a Special Class of Conformal Killing Tensors of Arbitrary Valence.” Reports on Mathematical Physics 62 (2): 241–254.
Vancouver
1.
Crampin M. Structural equations for a special class of conformal Killing tensors of arbitrary valence. REPORTS ON MATHEMATICAL PHYSICS. 2008;62(2):241–54.
IEEE
[1]
M. Crampin, “Structural equations for a special class of conformal Killing tensors of arbitrary valence,” REPORTS ON MATHEMATICAL PHYSICS, vol. 62, no. 2, pp. 241–254, 2008.
@article{663259,
  abstract     = {A symmetric tensor T on a (pseudo-)Riemannian manifold which satisfies T-i1,(i2),....,(irij) = S((i1),(i2),....,(ir-1)g(ir))j for some symmetric tensor S is a conformal Killing tensor of a special kind. Such special conformal Killing tensors of valence I and 2 have been extensively studied. In this paper special conformal Killing tensors of arbitrary valence, and indeed certain non-metrical generalizations of them, are investigated. In particular, it is shown that the space of special conformal Killing tensors is finite dimensional, and the maximal dimension is attained (in the (pseudo-)Riemannian case) if and only if the manifold is a space of constant curvature. This result is obtained by constructing a set of structural equations for special conformal Killing tensors.},
  author       = {Crampin, Michael},
  issn         = {0034-4877},
  journal      = {REPORTS ON MATHEMATICAL PHYSICS},
  language     = {eng},
  number       = {2},
  pages        = {241--254},
  title        = {Structural equations for a special class of conformal Killing tensors of arbitrary valence},
  url          = {http://dx.doi.org/10.1016/S0034-4877(08)80029-8},
  volume       = {62},
  year         = {2008},
}

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