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

Annales UMCS, Mathematica (2015)

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

## Access Full Article

top## Abstract

top## How to cite

topGrzegorz 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

top- [1] Besse, A., Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, 1987.
- [2] Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259-280. Zbl0378.53018
- [3] Jelonek, W., On A-tensors in Riemannian geometry, preprint PAN 551, 1995.
- [4] Jelonek, W., K-contact A-manifolds, Colloq. Math. 75 (1) (1998), 97-103. Zbl0893.53018
- [5] Jelonek, W., Almost K¨ahler A-structures on twistor bundles, Ann. Glob. Anal. Geom. 17 (1999), 329-339. Zbl0982.53045
- [6] Kobayashi, S., Principal fibre bundles with the 1-dimensional toroidal group, Tohoku Math. J. 8 (1956), 29-45. Zbl0075.32103
- [7] Moroianu, A., Semmelmann, U., Twistor forms on K¨ahler manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003), 823-845. Zbl1121.53050
- [8] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469.
- [9] Pedersen, H., Todd, P., The Ledger curvature conditions and D’Atri geometry, Differential Geom. Appl. 11 (1999), 155-162. Zbl0944.53025
- [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] Semmelmann, U., Conformal Killing forms on Riemannian manifolds, preprint, arXiv:math/0206117.
- [12] Tang, Z., Yan, W., Isoparametric foliation and a problem of Besse on generalizations of Einstein condition, preprint, arXiv:math/1307.3807.
- [13] Wang, M. Y., Ziller, W., Einstein metrics on torus bundles, J. Differential Geom. 31 (1990), 215-248. Zbl0691.53036
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.