Almost Complex and Almost Product Einstein Manifolds from a Variational Principle

Abstract

It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-Hermitian metric on a complex manifold satisfies the Kähler condition on the same manifold treated as a real manifold if and only if the metric is the real part of a holomorphic metric. A characterisation of anti-Kähler Einstein manifolds and almost-product Einstein manifolds is obtained. Examples of such manifolds are considered.

31 pages, Latex

References in corpus (2)

• Product Einstein Manifolds, Zeta-Function Regularization and the Multiplicative Anomaly
• Split structures in general relativity and the Kaluza-Klein theories

Cited by in corpus (8)

• Accelerated Cosmological Models in Ricci squared Gravity
• Ghosts in pure and hybrid formalisms of gravity theories: a unified analysis
• Sasaki-like almost contact complex Riemannian manifolds
• From Spinor Geometry to Complex General Relativity
• Anti-Kählerian geometry on Lie groups
• On 4-dimensional, conformally flat, almost $\epsilon$-Kählerian manifolds
• A note on para-holomorphic Riemannian Einstein manifolds
• Invariant tensors under the twin interchange of the pairs of the associated metrics on almost paracomplex pseudo-Riemannian manifolds