Killing tensors and warped product
Jelonek, Włodzimierz
Annales Polonici Mathematici, Tome 75 (2000), p. 15-33 / Harvested from The Polish Digital Mathematics Library

We present some examples of Killing tensors and give their geometric interpretation. We give new examples of non-compact complete and compact Riemannian manifolds whose Ricci tensor ϱ satisfies the condition Xϱ(X,X)=2/(n+2)Xτg(X,X)

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:208380
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     title = {Killing tensors and warped product},
     journal = {Annales Polonici Mathematici},
     volume = {75},
     year = {2000},
     pages = {15-33},
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Jelonek, Włodzimierz. Killing tensors and warped product. Annales Polonici Mathematici, Tome 75 (2000) pp. 15-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z1p15bwm/

[000] [B] A. Besse, Einstein Manifolds, Springer, Berlin, 1987

[001] [D] A. Derdziński, Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, Math. Z. 172 (1980), 273-280 | Zbl 0453.53037

[002] [G] A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259-280. | Zbl 0378.53018

[003] [H] S. Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), 209-215. | Zbl 0387.53014

[004] [J-1] W. Jelonek, On A-tensors in Riemannian geometry, preprint 551, Polish Academy of Sciences, 1995.

[005] [J-2] W. Jelonek, Killing tensors and Einstein-Weyl geometry, Colloq. Math. 81 (1999), 5-19. | Zbl 0945.53028

[006] [K-N] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience, New York, 1963. | Zbl 0119.37502

[007] [M-P-P-S] B. Madsen, H. Pedersen, Y. Poon and A. Swaan, Compact Einstein-Weyl manifolds with large symmetry group, Duke Math. J. 88 (1997), 407-434. | Zbl 0881.53041

[008] [N] S. Nölker, Isometric immersions of warped products, Differential Geom. Appl. 6 (1996), 1-30. | Zbl 0881.53052

[009] [O'N] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469.