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CONFORMAL TRANSFORMATIONS IN A TWISTED PRODUCT SPACE

  • KIM, BYUNG-HAK ;
  • JUNG, SEOUNG-DAL ;
  • KANG, TAE-HO ;
  • PAK, HONG-KYUNG
  • Published : 2005.02.01

Abstract

The conharmonic transformation is a conformal trans-formation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishii and we have generalized his results. Twisted product space is a generalized warped product space with a warping function defined on a whole space. In this paper, we partially classified the twisted product space and obtain a sufficient condition for a twisted product space to be locally Riemannian products.

Keywords

conformally flat;conharmonic transformation;twisted product space

References

  1. B. H. Kim, I. B. Kim, and S. M. Lee, Conharmonic transformation and critical Riemannian metrics, Commun. Korean Math. Soc. 12 (1997), 347-354
  2. Y. Agaoka and B. H. Kim, On conformally flat twisted product manifold, Mem. Fac. Imt. Arts and Sci., Hiroshima Univ. 23 (1997), 1-7
  3. A. Besse, Einstein manifolds, Springer, Berlin, 1987
  4. B. Y. Chen, Totally umbilical submanifolds, Soochow J. Math. 5 (1979), 9-37
  5. Y. Ishii, On conharmonic transformation, Tensor (N.S.) 7 (1957), 73-80
  6. M. F. Lopez, E. Garcia-Rio, D. N. Kupeli, and B. Unal, A curvature condition for a twisted product to be a warped product, Manuscripta Math. 106 (2001), 213--217 https://doi.org/10.1007/s002290100204
  7. Y. Machida and H. Sato, Twistor spaces for real four-dimensional Lorentzian manifolds, Nagoya Math. J. 134 (1994), 107-135
  8. P. Peterser, Riemannian geometry, Springer, Berlin, 1997
  9. R. Ponge and H. Reckziegel, Twisted products in pseudo-Riemannian geometry, Geom. Dedicata 48 (1993), 15-25
  10. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251-275
  11. K. Yano, Concircular geometry, I, II, III, IV, Proc. Imp. Acad. Tokyo 16 (1940), 195-200, 354-360, 442-448, 505-511
  12. K. Yano, Concircular geometry, I, II, III, IV, Proc. Imp. Acad. Tokyo 18 (1942), 446-451