Amici, Oriella and Casciaro, Biagio and Francaviglia, Mauro (2004) Second Variation and Generalized Jacobi Equations for Curvature Invariants. Anno 1996, LXXIV. pp. 73-102.
We consider the second variation and the appropriate Jacobi eqautions for the scalar curvature and the quadratic curvature invariants based on an independent pair (g, T) formed by a metric and torsionless linear connection (so-called 'Palatini formalism'). The purely metric case is obtained as a consequence. The results are worked out in fill detail in view of applications to non-linear Lagrangian theories of gravitation.
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