Journal of the
Korean Mathematical Society JKMS

In the present paper, we introduce the notions of quaternionically planar curves and quaternionically projective transformations to the case of almost quaternionic manifold with symmetric affine connection. Also, we obtain an invariant tensor field under the quaternionically projective transformation, and show that a quaternionic K\"ahlerian manifold with such a vanishing tensor field is of constant $Q$-sectional curvature.

Keywords: almost quaternionic manifold, quaternionic projective transformation, quaternionic Kaherian manifold

MSC numbers: 53C25