Covariant second variation for first order Lagrangians on fibered manifolds II: generalized curvature and Bianchi identities

Abstract

The notion of generalized curvature structures ensuing from the second variation of a (first–order) Lagrangian is extensively discussed. It is shown that generalized curvature structures satisfy appropriate (generalized) Bianchi identities. Formulae applicable to curvature Lagrangians are developed in great detail. Examples are taken from the theory of generalized harmonic Lagrangians.

Keywords

• second variation
• generalized curvature tensorfields
• bianchi identities