Abstract
An almost Hermitian manifold (,J, g) with Riemannian connectionis callednearly Kaehlerianif (xJ)X= 0 for any. The typical example is the sphereS6. The nearly Kaehlerian structureJforS6is constructed in a natural way by making use of Cayley division algebra [3]. It is because of this nearly Kaehler, non-Kaehler, structure thatS6has attracted attention. Different classes of submanifolds ofS6have been considered by A. Gray [4], K. Sekigawa [5] and N. Ejiri [2]. In this paper we study 2-dimensional totally real submanifolds ofS6. These are submanifolds with the property that for everyx є M, J(TxM) belongs to the normal bundle v. For this class we have obtained the following result.
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