A-manifolds on a principal torus bundle over an almost Hodge A-manifold base

Grzegorz Zborowski

Annales UMCS, Mathematica (2015)

  • Volume: 69, Issue: 1, page 109-119
  • ISSN: 2083-7402

Abstract

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An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇XXRic(X,X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds

How to cite

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Grzegorz Zborowski. "A-manifolds on a principal torus bundle over an almost Hodge A-manifold base." Annales UMCS, Mathematica 69.1 (2015): 109-119. <http://eudml.org/doc/270911>.

@article{GrzegorzZborowski2015,
abstract = {An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇XXRic(X,X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds},
author = {Grzegorz Zborowski},
journal = {Annales UMCS, Mathematica},
keywords = {and phrases. A-manifold; cyclic parallel Ricci; torus bundle; Einstein-like manifold; Killing tensor; -manifold},
language = {eng},
number = {1},
pages = {109-119},
title = {A-manifolds on a principal torus bundle over an almost Hodge A-manifold base},
url = {http://eudml.org/doc/270911},
volume = {69},
year = {2015},
}

TY - JOUR
AU - Grzegorz Zborowski
TI - A-manifolds on a principal torus bundle over an almost Hodge A-manifold base
JO - Annales UMCS, Mathematica
PY - 2015
VL - 69
IS - 1
SP - 109
EP - 119
AB - An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇XXRic(X,X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds
LA - eng
KW - and phrases. A-manifold; cyclic parallel Ricci; torus bundle; Einstein-like manifold; Killing tensor; -manifold
UR - http://eudml.org/doc/270911
ER -

References

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  10. [10] Sekigawa, K., Vanhecke, L., Symplectic geodesic symmetries on K¨ahler manifolds, Quart. J. Math. Oxford Ser. (2) 37 (1986), 95-103. Zbl0589.53068
  11. [11] Semmelmann, U., Conformal Killing forms on Riemannian manifolds, preprint, arXiv:math/0206117. 
  12. [12] Tang, Z., Yan, W., Isoparametric foliation and a problem of Besse on generalizations of Einstein condition, preprint, arXiv:math/1307.3807. 
  13. [13] Wang, M. Y., Ziller, W., Einstein metrics on torus bundles, J. Differential Geom. 31 (1990), 215-248. Zbl0691.53036
  14. [14] Zborowski, G., Construction of an A-manifold on a principal torus bundle, Ann. Univ. Paedagog. Crac. Stud. Math. 12 (2013), 5-19. Zbl1303.53059

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