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Almost-complex and almost-product Einstein manifolds from a variational principle (1999)

Borowiec, Andrzej ; Ferraris, Marco ; Francaviglia, Mauro ; [et al.]

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 40 (1999), S. 3446-3464

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: 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 characterization of anti-Kähler Einstein manifolds and almost-product Einstein manifolds is obtained. Examples of such manifolds are considered. © 1999 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.532899

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