Construction of an $A$-manifold on a principal torus bundle
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Autor:
Zborowski, Grzegorz
Źródło: Annales Universitatis Paedagogicae Cracoviensis. 128, Studia Mathematica 12 (2013), s. [5]-19
Język: en
Słowa kluczowe:
$A$-manifoldtorus bundle
Ricci tensor
Data: 2013
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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 a product of Kähler-Einstein
manifolds with fibre a torus of arbitrary dimension.