Some indefinite metrics and covariant derivatives of their curvature tensors

W. Roter

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 2, page 283-292
  • ISSN: 0010-1354

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Roter, W.. "Some indefinite metrics and covariant derivatives of their curvature tensors." Colloquium Mathematicae 62.2 (1991): 283-292. <http://eudml.org/doc/210115>.

@article{Roter1991,
author = {Roter, W.},
journal = {Colloquium Mathematicae},
keywords = {indefinite metrics; pseudo-Riemannian manifolds},
language = {eng},
number = {2},
pages = {283-292},
title = {Some indefinite metrics and covariant derivatives of their curvature tensors},
url = {http://eudml.org/doc/210115},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Roter, W.
TI - Some indefinite metrics and covariant derivatives of their curvature tensors
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 2
SP - 283
EP - 292
LA - eng
KW - indefinite metrics; pseudo-Riemannian manifolds
UR - http://eudml.org/doc/210115
ER -

References

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  1. [1] T. Adati and T. Miyazawa, On a Riemannian space with recurrent conformal curvature, Tensor (N.S.) 18 (1967), 348-354. Zbl0152.39103
  2. [2] M. C. Chaki and B. Gupta, On conformally symmetric spaces, Indian J. Math. 5 (1963), 113-122. Zbl0122.39902
  3. [3] A. Derdziński, The local structure of essentially conformally symmetric manifolds with constant fundamental function, I. The elliptic case, Colloq. Math. 42 (1979), 53-81. Zbl0439.53034
  4. [4] A. Derdziński, The local structure of essentially conformally symmetric manifolds with constant fundamental function, II. The hyperbolic case, ibid. 44 (1981), 77-95. Zbl0491.53013
  5. [5] A. Derdziński and W. Roter, On conformally symmetric manifolds with metrics of indices 0 and 1, Tensor (N.S.) 31 (1977), 255-259. Zbl0379.53027
  6. [6] A. Derdziński and W. Roter, Some theorems on conformally symmetric manifolds, ibid. 32 (1978), 11-23. Zbl0378.53010
  7. [7] L. P. Eisenhart, Riemannian Geometry, 2nd ed., Princeton University Press, Princeton 1949. 
  8. [8] V. R. Kaĭgorodov, Structure of the curvature of space-time, in: Problems in Geometry, Itogi Nauki i Tekhniki 14 (1983), 177-204 (in Russian). 
  9. [9] M. Matsumoto, On Riemannian spaces with recurrent projective curvature, Tensor (N.S.) 19 (1968), 11-18. Zbl0168.19405
  10. [10] H. K. Nickerson, On conformally symmetric spaces, Geom. Dedicata 18 (1985), 87-99. Zbl0568.53013
  11. [11] K. Nomizu and H. Ozeki, A theorem on curvature tensor fields, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 206-207. Zbl0139.39201
  12. [12] E. M. Patterson, Some theorems on Ricci-recurrent spaces, J. London Math. Soc. 27 (1952), 287-295. Zbl0048.15604
  13. [13] W. Roter, On conformally related conformally recurrent metrics, I. Some general results, Colloq. Math. 47 (1982), 39-46. Zbl0512.53021
  14. [14] W. Roter, On a class of conformally recurrent manifolds, Tensor (N.S.) 39 (1982), 207-217. Zbl0518.53018
  15. [15] W. Roter, On the existence of certain conformally recurrent metrics, Colloq. Math. 51 (1987), 315-327. Zbl0622.53012
  16. [16] H. S. Ruse, A. G. Walker and T. J. Willmore, Harmonic Spaces, Edizioni Cremonese, Roma 1961. Zbl0134.39202
  17. [17] S. Tanno, Curvature tensors and covariant derivatives, Ann. Mat. Pura Appl. 96 (1973), 233-241. Zbl0277.53013
  18. [18] A. G. Walker, On Ruse's spaces of recurrent curvature, Proc. London Math. Soc. 52 (1950), 36-64. Zbl0039.17702

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