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In general relativity and tensor calculus, the Palatini identity is: where denotes the variation of Christoffel symbols and indicates covariant differentiation. A proof can be found in the entry Einstein–Hilbert action. The "same" identity holds for the Lie derivative . In fact, one has: where denotes any vector field on the spacetime manifold .

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  • Identitat de Palatini (ca)
  • Identità di Palatini (it)
  • Palatini identity (en)
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  • En matemàtiques, la identitat de Palatini és una expressió, derivada pel matemàtic italià A. Palatini, emprada en teoria de la relativitat i càlcul tensorial: on denota la variació dels i indica la derivada covariant. La identitat es pot derivar a partir de l'. La "mateixa" identitat funciona per a la : on denota qualsevol camp vectorial a la varietat d'espaitemps . (ca)
  • In general relativity and tensor calculus, the Palatini identity is: where denotes the variation of Christoffel symbols and indicates covariant differentiation. A proof can be found in the entry Einstein–Hilbert action. The "same" identity holds for the Lie derivative . In fact, one has: where denotes any vector field on the spacetime manifold . (en)
  • In relatività generale e nel calcolo tensoriale, l'identità di Palatini, dovuta al matematico Attilio Palatini, è definita dalla formula: dove denota la variazione dei simboli di Christoffel e denota la derivata covariante. Una analoga, pressoché identica, formula vale per la derivata di Lie . Infatti, si ha: dove denota un qualsiasi campo vettoriale definito sopra lo spaziotempo. (it)
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  • En matemàtiques, la identitat de Palatini és una expressió, derivada pel matemàtic italià A. Palatini, emprada en teoria de la relativitat i càlcul tensorial: on denota la variació dels i indica la derivada covariant. La identitat es pot derivar a partir de l'. La "mateixa" identitat funciona per a la : on denota qualsevol camp vectorial a la varietat d'espaitemps . (ca)
  • In general relativity and tensor calculus, the Palatini identity is: where denotes the variation of Christoffel symbols and indicates covariant differentiation. A proof can be found in the entry Einstein–Hilbert action. The "same" identity holds for the Lie derivative . In fact, one has: where denotes any vector field on the spacetime manifold . (en)
  • In relatività generale e nel calcolo tensoriale, l'identità di Palatini, dovuta al matematico Attilio Palatini, è definita dalla formula: dove denota la variazione dei simboli di Christoffel e denota la derivata covariante. Una analoga, pressoché identica, formula vale per la derivata di Lie . Infatti, si ha: dove denota un qualsiasi campo vettoriale definito sopra lo spaziotempo. (it)
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