Dimensional curvature identities on pseudo-Riemannian geometry

作者：Navarro Alberto; Navarro Jose^*

来源：Journal of Geometry and Physics, 2014, 86: 554-563.

DOI：10.1016/j.geomphys.2014.10.001

• Curvature identities
• Riemannian geometry
• Lovelock tensors

For a fixed n is an element of N, the curvature tensor of a pseudo-Riemannian metric, as well as its covariant derivatives, satisfies certain identities that hold on any manifold of dimension less than or equal to n. %26lt;br%26gt;In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa regarding these p-covariant curvature identities, for p = 0, 2. To this end, we use the classical theory of natural operations that allows us to simplify some arguments and to generalize the description of Gilkey-Park-Sekigawa, both by dropping a symmetry hypothesis and by including p-covariant curvature identities, for any even p. %26lt;br%26gt;Thus, for any dimension n, our main result describes the first space (i.e., that of highest weight) of p-covariant dimensional curvature identities, for any even p.

• 出版日期2014-12