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Annals of Global Analysis and Geometry

, Volume 45, Issue 1, pp 11–24 | Cite as

Conical Ricci-flat nearly para-Kähler manifolds

  • Lars SchäferEmail author
Article

Abstract

In this paper, we classify conical Ricci-flat nearly para-Kähler manifolds having isotropic Nijenhuis tensor. More precisely, we give a bijective correspondence between this class of nearly para-Kähler manifolds and local cones \(M_1 \times (a,b)\) over para-Sasaki-Einstein manifolds \((M_1,g_1,T)\) carrying a parallel 3-form with isotropic support. Moreover, we show that the cone over a para-Sasaki-Einstein five-manifold \((M_1,g_1,T)\) admits a family of parallel 3-forms with isotropic support. As an application our result yields first examples of Ricci-flat (non-flat) nearly para-Kähler structures.

Keywords

Nearly para-Kähler manifold Ricci-flat Semi-Riemannian metrics 

Mathematics Subject Classification (2000)

53C15 53C28 53C29 53C25 53C26 

Notes

Acknowledgments

The author thanks Lutz Habermann and the unkown referee for valuable comments on earlier versions of the manuscript and Florin Belgun and Vicente Cortés for interest and remarks during a research stay at Hamburg.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut für DifferentialgeometrieLeibniz Universität HannoverHannoverGermany

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