QR-submanifolds of a locally conformal quaternion Kaehler manifold


Sahin B., Gunes R.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.63, pp.157-174, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63
  • Publication Date: 2003
  • Title of Journal : PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Page Numbers: pp.157-174

Abstract

In this paper, we study QR-submanifolds of a locally conformal quaternion Kaehler manifold. We give the basic formulas for QR-submanifolds of a locally conformal quaternion Kaehler manifold and two examples of QR-submanifolds of a locally conformal quaternion Kaehler manifold. Necessary and sufficient conditions are given for a quaternion distribution on a QR-submanifold to be integrable. Also, a necessary and sufficient condition is given for a distribution D-perpendicular to on a QR-submanifold to be a totally geodesic foliation. Further, a theorem is obtained for a QR-submanifold to be mixed geodesic. Finally, totally umbilical QR-submanifolds are studied and some theorems are given.