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## Online first articles

Articles are posted here individually soon after proof is returned from authors, before the corresponding journal issue is completed. All articles are in their final form, including issue number and pagination. For recently accepted articles, see Articles in press.

 $\mathfrak{D}^\perp$-invariant real hypersurfaces in complex Grassmannians of rank two. Ruenn-Huah Lee and Tee-How Loo Let $M$ be a real hypersurface in a complex Grassmannian of rank two. Denote by $\mathfrak{J}$ the quaternionic Kähler structure of the ambient space, $TM^\perp$ the normal bundle over $M$, and $\mathfrak{D}^\perp=\mathfrak{J}TM^\perp$. The real hypersurface $M$ is said to be $\mathfrak{D}^\perp$-invariant if $\mathfrak{D}^\perp$ is invariant under the shape operator of $M$. We show that if $M$ is $\mathfrak{D}^\perp$-invariant, then $M$ is Hopf. This improves the results of Berndt and Suh [Int. J. Math. 23 (2012) 1250103] and [Monatsh. Math. 127 (1999), 1–14]. We also classify $\mathfrak{D}^\perp$ real hypersurfaces in complex Grassmannians of rank two of noncompact type with constant principal curvatures. 197–207