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Journal of the London Mathematical Society Advance Access originally published online on October 16, 2009
Journal of the London Mathematical Society 2009 80(3):729-749; doi:10.1112/jlms/jdp050
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© 2009 London Mathematical Society

Higher-dimensional Gray Hermitian manifolds

Wlodzimierz Jelonek

Institute of Mathematics
Cracow University of Technology
Warszawska 24
31-155 Kraków
Poland

The aim of this paper is to classify compact, Riemannian, Hermitian conformally Kähler manifolds (M, g, J) whose Ricci tensor {rho} is J-invariant and satisfies the condition that {rho} – (2{tau}/(dim M + 2))g is a Killing tensor, where {tau} is the scalar curvature of (M, g). We classify such manifolds whose Ricci tensor has two eigenvalues and two-dimensional, totally geodesic eigendistribution.

2000 Mathematics Subject Classification 53C55, 53C25.

Received December 6, 2008; revised May 19, 2009; published online October 16, 2009.


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