Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON SEMI-RIEMANNIAN MANIFOLDS SATISFYING THE SECOND BIANCHI IDENTITY

  • Kwon, Jung-Hwan (Department of Mathematics Education Taegu University) ;
  • Pyo, Yong-Soo (Division of Mathematical Sciences Pukyung National University) ;
  • Suh, Young-Jin (Department of Mathematics Kyungpook National University)
  • Published : 2003.01.01
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Abstract

In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concircular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in [18] and [19].

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References

  1. Kodai. Math. J v.11 Semi-Kaehleran submanifolds of an indefinite complex space form R. Aiyama;H. Nakagawa;Y. J. Suh https://doi.org/10.2996/kmj/1138038931
  2. J. Differential Geometry v.3 Some characterizations of the space of symmetric tensors on a Riemannian manifold M. Berger;D. Ebin https://doi.org/10.4310/jdg/1214429060
  3. Einstein manifolds A. L. Besse
  4. Invent. Math. v.63 Les varietes de dimension 4 a signature non nulle don't la courbure et harmonique sont d'Einstein J. P. Bourguignon
  5. Rocky Mountain J. Math. v.31-2 On semi-symmetric complex hypersurfaces of a semi-definite complex space form Y. S. Choi;J.-H. Kwon;Y. J. Suh
  6. Rocky Mountain J. Math. v.31-3 On semi-Ryan complex submanifolds in an indefinite complex space form Y. S. Choi;J.-H. Kwon;Y. J. Suh
  7. Lecture Notes No. 838 Some remarks on the local structure of Codazzi tensors, in global differential geometry and global analysis A. Derdzinski
  8. Math. Ann. v.259 On compact Riemannian manifolds with harmonic curvature A. Derdzinski https://doi.org/10.1007/BF01457307
  9. Comp. Math. v.49 Self-dual K$\"{a}$hler manifolds and Einstein manifolds of codimension 4 A. Derdzinski
  10. Tensor, N. S. v.31 On conformally symmetric manifolds with metrics of indices 0 and 1 A. Derdzinski;W. Roter
  11. London Math. Soc. v.47 Codazzi tensor field, curvature and Pontrjagin forms A. Derdzinski;C. L. Shen https://doi.org/10.1112/plms/s3-47.1.15
  12. Geom. Dedicata v.7 Einstein-like manifolds which are not Einstein A. Gray
  13. J. Korean Math. Soc. v.28 Hypersurfaces wilth harmonic Weyl tensor of a real space form U-Hang Ki;H. Nakagawa
  14. Foundations of differential geometry, Ⅰand Ⅱ S. Kobayashi;K. Nomizu
  15. Semi-Riemannian Geometry with applications to relativity B. O'Neill
  16. Proc. 13th bianual Seminar Canada Math. Congress v.2 A note on conformally flat spaces with constant scalar curvature P. J. Ryan
  17. Houston J. Math. v.28 On space-like hypersurfaces with constant mean curvature in a Lorentz manifold Y. J. Suh;Y. S. Choi;H. Y. Yang
  18. Math. Z. v.26 Reine infinitesimaly geometrie H. Weyl
  19. Zur infinitesimaly geometrie : Einordnung der prrojektiren und der Auffussung H. Weyl
  20. The theory of Lie derivatives and its applications K. Yano
  21. Integral Formulas in Riemannian Geometry K. Yano
  22. Ann. of Math. Studies v.32 Curvature and Betti numbers K. Yano;S. Bochner
  23. Series in Pure Math. Structures on manifolds K. Yano;M. Kon

Cited by

  1. Conformally symmetric semi-Riemannian manifolds vol.56, pp.5, 2006, https://doi.org/10.1016/j.geomphys.2005.05.005
  2. Curvature properties of Robinson–Trautman metric vol.109, pp.2, 2018, https://doi.org/10.1007/s00022-018-0443-1