# De Donder Form for Second Order Gravity

## TL;DR

This paper demonstrates that the De Donder form for second order gravity can be globally defined using local coordinate descriptions, providing a natural differential operator for the theory's invariant Lagrangian.

## Contribution

It introduces a globally defined De Donder form for second order gravity based on Ostrogradski's Legendre transformation, enhancing the geometric understanding of the theory.

## Key findings

- De Donder form is globally defined for second order gravity.
- The form is constructed via Ostrogradski's Legendre transformation.
- It provides a natural differential operator for the invariant Lagrangian.

## Abstract

We show that the De Donder form for second order gravity, defined in terms of Ostrogradski's version of the Legendre transformation applied to all independent variables, is globally defined by its local coordinate descriptions. It is a natural differential operator applied to the diffeomorphism invariant Lagrangian of the theory.