Killing tensors and warped product

Włodzimierz Jelonek

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 15-33
  • ISSN: 0066-2216

Abstract

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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 ∇ X ϱ ( X , X ) = 2 / ( n + 2 ) X τ g ( X , X )

How to cite

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Jelonek, Włodzimierz. "Killing tensors and warped product." Annales Polonici Mathematici 75.1 (2000): 15-33. <http://eudml.org/doc/208380>.

@article{Jelonek2000,
abstract = {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 $∇_\{X\} ϱ(X,X) = 2/(n+2) Xτg(X,X)$},
author = {Jelonek, Włodzimierz},
journal = {Annales Polonici Mathematici},
keywords = {Ricci tensor; Killing tensor; Einstein manifold; warped product},
language = {eng},
number = {1},
pages = {15-33},
title = {Killing tensors and warped product},
url = {http://eudml.org/doc/208380},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Jelonek, Włodzimierz
TI - Killing tensors and warped product
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 15
EP - 33
AB - 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 $∇_{X} ϱ(X,X) = 2/(n+2) Xτg(X,X)$
LA - eng
KW - Ricci tensor; Killing tensor; Einstein manifold; warped product
UR - http://eudml.org/doc/208380
ER -

References

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  1. [B] A. Besse, Einstein Manifolds, Springer, Berlin, 1987 
  2. [D] A. Derdziński, Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, Math. Z. 172 (1980), 273-280 Zbl0453.53037
  3. [G] A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259-280. Zbl0378.53018
  4. [H] S. Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), 209-215. Zbl0387.53014
  5. [J-1] W. Jelonek, On A-tensors in Riemannian geometry, preprint 551, Polish Academy of Sciences, 1995. 
  6. [J-2] W. Jelonek, Killing tensors and Einstein-Weyl geometry, Colloq. Math. 81 (1999), 5-19. Zbl0945.53028
  7. [K-N] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience, New York, 1963. Zbl0119.37502
  8. [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. Zbl0881.53041
  9. [N] S. Nölker, Isometric immersions of warped products, Differential Geom. Appl. 6 (1996), 1-30. Zbl0881.53052
  10. [O'N] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. 

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