International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2575

Full Length Research Paper

Almost quaternionic integral submanifolds and totally umbilic integral submanifolds

Fatma Özdemir
Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, 34469 Maslak-Istanbul, Turkey
Email: [email protected]

  •  Accepted: 22 August 2013
  •  Published: 30 August 2013

Abstract

In this work, we consider a Riemannian manifold which admits an integrable distribution  with an almost quaternionic structure V. We show that the torsion tensor of an almost quaternionic structure  is independent of the choice of bases. We prove that the integral submanifolds are totally umbilic under the condition of the conjugate shape operator is skew-adjoint. We give another condition for the shape operator  of  to be quaternionic linear.

 

Key words: Subbundle, almost complex structure, almost quaternionic structure, shape operator.