A-manifolds on a principal torus bundle over an almost Hodge A-manifold base
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2015)
- Volume: 69, Issue: 1
- ISSN: 0365-1029
Access Full Article
top
Abstract
topHow to cite
topGrzegorz Zborowski. "A-manifolds on a principal torus bundle over an almost Hodge A-manifold base." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 69.1 (2015): null. <http://eudml.org/doc/289750>.
@article{GrzegorzZborowski2015,
abstract = {An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇X Ric(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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {A-manifold; cyclic parallel Ricci; torus bundle; Einstein-like manifold; Killing tensor},
language = {eng},
number = {1},
pages = {null},
title = {A-manifolds on a principal torus bundle over an almost Hodge A-manifold base},
url = {http://eudml.org/doc/289750},
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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2015
VL - 69
IS - 1
SP - null
AB - An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇X Ric(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 - A-manifold; cyclic parallel Ricci; torus bundle; Einstein-like manifold; Killing tensor
UR - http://eudml.org/doc/289750
ER -
References
top- Besse, A., Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, 1987.
- Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259–280.
- Jelonek, W., On A-tensors in Riemannian geometry, preprint PAN 551, 1995.
- Jelonek, W., K-contact A-manifolds, Colloq. Math. 75 (1) (1998), 97–103.
- Jelonek, W., Almost Kahler A-structures on twistor bundles, Ann. Glob. Anal. Geom. 17 (1999), 329–339.
- Kobayashi, S., Principal fibre bundles with the 1-dimensional toroidal group, Tohoku Math. J. 8 (1956), 29–45.
- Moroianu, A., Semmelmann, U., Twistor forms on Kahler manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003), 823–845.
- O’Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469.
- Pedersen, H., Todd, P., The Ledger curvature conditions and D’Atri geometry, Differential Geom. Appl. 11 (1999), 155–162.
- Sekigawa, K., Vanhecke, L., Symplectic geodesic symmetries on K¨ahler manifolds, Quart. J. Math. Oxford Ser. (2) 37 (1986), 95–103.
- Semmelmann, U., Conformal Killing forms on Riemannian manifolds, preprint, arXiv:math/0206117.
- Tang, Z., Yan, W., Isoparametric foliation and a problem of Besse on generalizations of Einstein condition, preprint, arXiv:math/1307.3807.
- Wang, M. Y., Ziller, W., Einstein metrics on torus bundles, J. Differential Geom. 31 (1990), 215–248.
- Zborowski, G., Construction of an A-manifold on a principal torus bundle, Ann. Univ. Paedagog. Crac. Stud. Math. 12 (2013), 5–19.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.