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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  );
  • 초록

    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.


  • 주제어

    conformally flat .   conharmonic transformation .   twisted product space.  

  • 참고문헌 (12)

    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 
    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 

 저자의 다른 논문

  • Kim, Byung-Hak (30)

    1. 1993 "A NEW CLASS OF ALMOST CONTACT RIEMANNIAN MANIFOLDS" Communications of the Korean Mathematical Society = 대한수학회논문집 8 (3): 455~465    
    2. 1993 "WARPED PRODUCT SPACES WITH EINSTEIN METRIC" Communications of the Korean Mathematical Society = 대한수학회논문집 8 (3): 467~473    
    3. 1993 "FIBRED RIEMANNIAN SPACES WITH K-CONTACT STRUCTURE" Communications of the Korean Mathematical Society = 대한수학회논문집 8 (3): 475~481    
    4. 1994 "FIBRED RIEMANNIAN SPACES WITH CRITICAL RIEMANNIAN METRICS" Journal of the Korean Mathematical Society = 대한수학회지 31 (2): 205~211    
    5. 1995 "Critical rimennian metrics on cosymplectic manifolds" Journal of the Korean Mathematical Society = 대한수학회지 32 (3): 553~562    
    6. 1995 "Totally real submanifolds with parallel mean curvature vector in a complex space form" Journal of the Korean Mathematical Society = 대한수학회지 32 (4): 835~848    
    7. 1995 "REMARKS ON SUBMANIFOLDS OF COSYMPLECTIC MANIFOLDS" Kangweon-Kyungki mathematical journal 3 (2): 233~240    
    8. 1997 "Conformally flat cosymplectic manifolds" Communications of the Korean Mathematical Society = 대한수학회논문집 12 (4): 999~1006    
    9. 1999 "FIBRED RIEMANNIAN SPACE WITH KENMOTSU STRUCTURE" Korean journal of computational & applied mathematics 6 (3): 921~928    
    10. 2000 "CONFORMALLY FLAT WARPED PRODUCT RIEMANNIAN MANIFOLDS" Korean journal of computational & applied mathematics 7 (1): 297~303    
  • Kang, Tae Ho (18)

  • Pak, Hong-Kyung (15)

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