International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Some classification results on totally umbilical proper slant and hemi-slant submanifolds of a nearly Kenmotsu manifold

Siraj Uddin1, Cenap Ozel2*, M. A. Khan3 and Khushwant Singh4
  1Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia. 2Department of Mathematics, Abant Izzet Baysal University, 14268 Bolu, Turkey. 3Department of Mathematics, University of Tabuk, 80015 Tabuk, Kingdom of Saudi Arabia. 4School of Mathematics and Computer Applications, Thapar University, 147004 Patiala, India.
Email: [email protected]

  •  Accepted: 14 May 2012
  •  Published: 23 October 2013

Abstract

 

This paper is concerned with the study of slant and hemi-slant submanifolds of a nearly Kenmotsu manifold. We prove that every totally umbilical proper slant submanifold of a nearly Kenmotsu manifold is totally geodesic and derive the integrability conditions of involved distributions in the definition of a hemi-slant submanifold. Finally, we obtain a classification theorem on a totally umbilical hemi-slant submanifold of a nearly Kenmotsu manifold.

 

Key words: Slant submanifold, hemi-slant submanifold, totally umbilical, minimal submanifold, nearly Kenmotsu manifold.

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