Construction of an A-manifold on a principal torus bundle

Grzegorz Zborowski

Abstract


We construct a new example of an A-manifold, i.e. a Riemannian manifold with cyclic-parallel Ricci tensor. This condition can be viewed as a generalization of the Einstein condition. The underlying manifold for our construction is a principal torus bundle over Kähler-Einstein manifold with fibre a torus of arbitrary dimension.

Keywords


A-manifold; torus bundle; Ricci tensor

Mathematics Subject Classification


53C25

References


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Wang, M.Y. and W. Ziller. "Einstein metrics on principal torus bundles." J. Differential Geom. 31 (1990): 215-248.


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