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- W985032875 abstract "Examples presented in this chapter include typical variational functionals that appear as variational principles in the theory of geometric and physical fields. We begin by the discussion of the well-known Hilbert variational functional for the metric fields, first considered in Hilbert in 1915, whose Euler–Lagrange equations are the Einstein vacuum equations. We give a manifold interpretation of this functional and show that its second-order Lagrangian, the formal scalar curvature, possesses a global first-order Lepage equivalent. The Lagrangian used by Hilbert is an example of a differential invariant of a metric field (and its first and second derivatives). Further examples with similar properties, belonging to the class of natural Lagrange structures, are also considered." @default.
- W985032875 created "2016-06-24" @default.
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- W985032875 date "2015-01-01" @default.
- W985032875 modified "2023-09-25" @default.
- W985032875 title "Examples: Natural Lagrange Structures" @default.
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- W985032875 doi "https://doi.org/10.2991/978-94-6239-073-7_6" @default.
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