QR-submanifolds of a locally conformal quaternion Kaehler manifold
Articles > Article · 2003
Authors: Bayram ŞAHİN, Rifat Günes
PUBLICATIONES MATHEMATICAE-DEBRECEN, Journal Indexed in SCI Expanded, International, Scopus, 2003, vol 63, pp 157-174
Summary
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⊥ 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.