Full Length Research Paper
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.
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