DOI QR코드

DOI QR Code

CONFORMAL TRANSFORMATIONS IN A TWISTED PRODUCT SPACE

  • KIM, BYUNG-HAK (Department of Mathematics and Institute of Natural Sciences, Kyung Hee University) ;
  • JUNG, SEOUNG-DAL (Department of Mathematics, Cheju University) ;
  • KANG, TAE-HO (Department of Mathematics, University of Ulsan) ;
  • PAK, HONG-KYUNG (Department of Information Security, Daegu Haany University)
  • 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.

References

  1. Y. Agaoka and B. H. Kim, On conformally flat twisted product manifold, Mem. Fac. Imt. Arts and Sci., Hiroshima Univ. 23 (1997), 1-7
  2. A. Besse, Einstein manifolds, Springer, Berlin, 1987
  3. B. Y. Chen, Totally umbilical submanifolds, Soochow J. Math. 5 (1979), 9-37
  4. Y. Ishii, On conharmonic transformation, Tensor (N.S.) 7 (1957), 73-80
  5. B. H. Kim, I. B. Kim, and S. M. Lee, Conharmonic transformation and critical Riemannian metrics, Commun. Korean Math. Soc. 12 (1997), 347-354
  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