Warped product semi-slant submanifolds in Kenmotsu manifolds

In this paper, we research the existence or non-existence of warped product semi-slant submanifolds in Kenmotsu manifolds. Consequently, we see that there are no proper warped product semi-slant submanifolds in Kenmotsu manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively.

Warped product semi-slant submanifolds in Kenmotsu manifolds

In this paper, we research the existence or non-existence of warped product semi-slant submanifolds in Kenmotsu manifolds. Consequently, we see that there are no proper warped product semi-slant submanifolds in Kenmotsu manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively.

___

  • Bishop, R.L. and O’Neill, B.: Manifolds of negative curvaure, Trans Amer. Math. Soc. 145, 1-49 (1969).
  • Cabrerizo, J.L., Carriazo, A. and L.M, Fernandez.: Slant submanifolds in Sasakian manifolds, Glasgow Math. J., , 125-138 (2000).
  • Cabrerizo, J.L., Carriazo, A., Fernandez, L.M. and Fernandez, M.: Structure on a slant submanifold of a contact manifold, Indian J. Pure and Appl. Math.,31(7), 857-864 (2000).
  • Chen, B.Y.: Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh Math. 133,177-195 (2001).
  • Chen, B.Y.: Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh Math. 134,103-119 (2001).
  • Chen, B.Y.: Geometry of slant submanifolds, Katholieke Universietit Leuven (1990).
  • Chen, B.Y.: Slant Immersions, Bull. Australian Math. Soc. 41, 135-147 (1990).
  • Gupta, R.S., Haider, S.M.K. and Shadid, M.H.: Slant submanifolds of a Kenmotsu manifold, Radovi Matematticki, Vol.12, 205-214 (2004).
  • Hasegawa, I. and Mihai, I.: Contact CR-Warped Product Submanifolds in Sasakian Manifolds, Geometriae Dedi- cata, 102, 143-150 (2003).
  • Khalid, A.K,, Khan, V.A. and Uddin, S.: Warped Product submanifolds of cosymplectic manifolds, Balkan Journal of Geometry and Its Appl, Vol. 13, No.1, pp.55-65 (2008).
  • Lotta, A.: Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 39, 183-198(1996).
  • Yano, K. and Kon, M.: Structure on manifolds. World ScientiŞc Publishing Co. Ltd (1984). Mehmet ATC¸ EKEN
  • Gaziosmanpasa University, Faculty of Arts and Sciences, Department of Mathematics, , Tokat-TURKEY e-mail: matceken@gop.edu.tr