QR-submanifolds of a locally conformal quaternion Kaehler manifold


ŞAHİN B. , GÜNEŞ R.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.63, ss.157-174, 2003 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 63
  • Basım Tarihi: 2003
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Sayfa Sayıları: ss.157-174

Özet

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.