대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권3호
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  • Pages.435-445
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  • 2005
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON KENMOTSU MANIFOLDS

  • JUN JAE-BOK (Department of Mathematics College of Natural Science Kookmin University) ;
  • DE UDAY CHAND (Department of Mathematics University of Kalyani) ;
  • PATHAK GOUTAM (Department of Mathematics University of Kalyani)
  • 발행 : 2005.05.01
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초록

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

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참고문헌

  1. K. Kenmotsu, A class of contact Riemannian manifold, Tohoku Math. Jour. 24 (1972), 93-103 https://doi.org/10.2748/tmj/1178241594
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  3. L. Verstraelen, Comments on pseudo-symmetry in the sence of R. Deszcz, Geometry and Topology of submanifolds VI , World Scientific, 1933, 199-209
  4. E.M. Patterson, Some theorems on Ricci recurrent spaces, J. London Math. Soc. 27 (1952), 287-295 https://doi.org/10.1112/jlms/s1-27.3.287
  5. D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1976
  6. B. ONeil, Semi-Riemannian geometry with application to relativity, Academic Press, p. 208
  7. M.C. Chaki and M. Tarafdar, On a type of Sasakian manifold, Soochow J. Math. 16 (1990), 23-28
  8. T. Adati and T. Miyazawa, On a Riemannian space with recurrent conformal curvature, Tensor (N.S.) 18 (1967), 348-354
  9. M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), 277-290 https://doi.org/10.1007/BF01354288
  10. S. Sasaki, Lecture notes on almost contact manifolds, Part II, Tohoku University, 1967

피인용 문헌

  1. Locally Symmetric CR-Integrable Almost Kenmotsu Manifolds vol.12, pp.1, 2015, https://doi.org/10.1007/s00009-014-0388-z
  2. On a type of almost Kenmotsu manifolds with nullity distributions vol.23, pp.2, 2017, https://doi.org/10.1016/j.ajmsc.2016.04.001
  3. On invariant submanifolds of Kenmotsu manifolds vol.106, pp.1, 2015, https://doi.org/10.1007/s00022-014-0238-y
  4. ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD vol.29, pp.2, 2014, https://doi.org/10.4134/CKMS.2014.29.2.331
  5. Some Curvature Properties of Kenmotsu Manifolds vol.85, pp.3, 2015, https://doi.org/10.1007/s40010-015-0215-3
  6. On lightlike geometry in indefinite Kenmotsu manifolds vol.62, pp.2, 2012, https://doi.org/10.2478/s12175-012-0012-2
  7. On Concircular Curvature Tensor with respect to the Semi-symmetric Non-metric Connection in a Kenmotsu Manifold vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.951
  8. Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians vol.40, pp.3, 2017, https://doi.org/10.1007/s40840-016-0372-9
  9. Almost Kenmotsu Pseudo-Metric Manifolds vol.0, pp.0, 2014, https://doi.org/10.2478/aicu-2014-0030
  10. )′-almost Kenmotsu manifolds vol.41, pp.4, 2018, https://doi.org/10.2989/16073606.2017.1391347