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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, ξ, η, ) with constant φ-sectional curvature c, such that the reeb vector field ξ 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 Kähler geometry.

 

 

 

 

 

 

 

 

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