대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권4호
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  • Pages.1273-1283
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  • 2018
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE PROPERTIES OF RIEMANNIAN FOLIATIONS ADMITTING TRANSVERSAL CONFORMAL FIELDS

  • 투고 : 2017.08.31
  • 심사 : 2018.01.29
  • 발행 : 2018.07.31
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초록

Let ($M,{\mathcal{F}}$) be a closed, oriented Riemannian manifold of a foliation ${\mathcal{F}}$ with a nonisometric transversal conformal field. Then ($M,{\mathcal{F}}$) is transversally isometric to the sphere under some transversal concircular curvature conditions.

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과제정보

연구 과제 주관 기관 : Jeju National University

참고문헌

  1. J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), no. 2, 179-194. https://doi.org/10.1007/BF00130919
  2. M. J. Jung and S. D. Jung, Riemannian foliations admitting transversal conformal fields, Geom. Dedicata 133 (2008), 155-168. https://doi.org/10.1007/s10711-008-9240-6
  3. S. D. Jung, Riemannian foliations admitting transversal conformal fields II, Geom. Dedicata 175 (2015), 257-266. https://doi.org/10.1007/s10711-014-0039-3
  4. S. D. Jung, K. R. Lee, and K. Richardson, Generalized Obata theorem and its applications on foliations, J. Math. Anal. Appl. 376 (2011), no. 1, 129-135. https://doi.org/10.1016/j.jmaa.2010.10.022
  5. F. W. Kamber and P. Tondeur, Harmonic foliations, in Harmonic maps (New Orleans, La., 1980), 87-121, Lecture Notes in Math., 949, Springer, Berlin, 1982.
  6. F. W. Kamber and P. Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, Tohoku Math. J. (2) 34 (1982), no. 4, 525-538. https://doi.org/10.2748/tmj/1178229154
  7. F. W. Kamber and P. Tondeur, de Rham-Hodge theory for Riemannian foliations, Math. Ann. 277 (1987), no. 3, 415-431. https://doi.org/10.1007/BF01458323
  8. J. Lee and K. Richardson, Lichnerowicz and Obata theorems for foliations, Pacific J. Math. 206 (2002), no. 2, 339-357. https://doi.org/10.2140/pjm.2002.206.339
  9. H. K. Pak and J. H. Park, A note on generalized Lichnerowicz-Obata theorems for Riemannian foliations, Bull. Korean Math. Soc. 48 (2011), no. 4, 769-777. https://doi.org/10.4134/BKMS.2011.48.4.769
  10. J. S. Pak and S. Yorozu, Transverse fields on foliated Riemannian manifolds, J. Korean Math. Soc. 25 (1988), no. 1, 83-92.
  11. J. S. Pak and S. Yorozu, Transversal conformal fields of foliations, Nihonkai Math. J. 4 (1993), no. 1, 73-85.
  12. P. Tondeur, Geometry of Foliations, Monographs in Mathematics, 90, Birkhauser Verlag, Basel, 1997.
  13. P. Tondeur and G. TTTth, On transversal infinitesimal automorphisms for harmonic foliations, Geom. Dedicata 24 (1987), no. 2, 229-236. https://doi.org/10.1007/BF00150938
  14. K. Yano, Concircular geometry. I. Concircular transformations, Proc. Imp. Acad. Tokyo 16 (1940), 195-200. https://doi.org/10.3792/pia/1195579139
  15. K. Yano, On Riemannian manifolds with constant scalar curvature admitting a conformal transformal transformations group, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 472-476. https://doi.org/10.1073/pnas.55.3.472
  16. K. Yano, Integral Formulas in Riemannian Geometry, Pure and Applied Mathematics, No. 1, Marcel Dekker, Inc., New York, 1970.
  17. S. Yorozu and T. Tanemura, Green's theorem on a foliated Riemannian manifold and its applications, Acta Math. Hungar. 56 (1990), no. 3-4, 239-245. https://doi.org/10.1007/BF01903838