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We study $n$-dimensional $QR$-submanifolds of $QR$-dimension $(p-1)$ immersed in a quaternionic space form $Q{P}^{(n+p)/4}\left(c\right)$, $c\geqq 0$, and, in particular, determine such submanifolds with the induced normal almost contact $3$-structure.

We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension $\ge 4$, and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on $p$ $(0\le p\le 2)$-forms on the manifold by using the traceless component....