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Vietnam Journal of Mathematics 33:2 (2005) 149-160 Submanifolds with Parallel Mean Curvature Vector Fields and Equal Wirtinger Angles in Sasakian Space Forms  Guanghan Li Abstract.  We study closed submanifolds $M$ of dimension $2n+1$, immersed into a $(4n+1)$-dimensional Sasakian space form $(N, \xi, \eta ,\varphi )$ with constant $\varphi $-sectional curvature $c$, such that the reeb vector field $\xi $ is tangent to $M$. Under the assumption that $M$ has equal Wirtinger angles and parallel mean curvature vector fields, we prove that for any positive integer $n$, $M$ is either an invariant or an anti-invariant submanifold of $N$ if $c> -3$, and the common Wirtinger angle must be constant if $c=-3$. Moreover, without assuming it being closed, we show that such a conclusion also holds for a slant submanifold $M$ (Wirtinger angles are constant along $M$) in the first case, which is very different from cases in K\"{a}hler geometry.

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