Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CONHARMONICALLY FLAT FIBRED RIEMANNIAN SPACE II

  • Lee, Sang-Deok (Department of Mathematics, Dankook University) ;
  • Kim, Byung-Hak (Department of Mathematics and Institute of Natural Sciences, Kyung Hee University)
  • Published : 2002.12.01

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Abstract

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

Keywords

References

  1. Mem. Fac. Integrated Arts and Sci. v.26 Conharmonically flat fibred Riemannian space Y.Agaoka;B.H.Kim;S.D.Lee
  2. J. Diff. Geom v.1 The theory of quasi-Sasakian structures D.E.Blair
  3. Lecture notes in Math. v.509 Contact manifolds in Riemannian geometry D.E.Blair
  4. Tensor N.S. v.7 On conharmonic transformation Y.Ishi
  5. Publ. study Group of Differential Geometry v.7 Differential geometry of fibred spaces S.Ishihara;M.Konishi
  6. Comm. Korean Math. Soc. v.12 Conharmonic transformation and critical Riemannian metrics B.H.Kim;I.B.Kim;S.M.Lee
  7. Hiroshima Math. v.20 Fibred Riemannian spaces with quasi Sasakian structure B.H.Kim
  8. Hiroshima Math. J. v.18 Almost complex and almost contact structures in fibred Riemanian spaces Y.Tashiro;B.H.Kim
  9. Comm. Korean Math. Soc. v.3 Fibred Riemannian spaecs with K-contact structure Y.Tashiro;B.H.Kim