Mathematics – Differential Geometry
Scientific paper
2010-11-25
Mathematics
Differential Geometry
14 pages
Scientific paper
We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to $2$ we define a second quadratic form with the same property and then determine those surfaces with parallel mean curvature vector on which the $(2,0)$-parts of both of them vanish. We also provide a reduction of codimension theorem and prove a non-existence result for $2$-spheres with parallel mean curvature vector.
No associations
LandOfFree
Surfaces with parallel mean curvature vector in complex space forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Surfaces with parallel mean curvature vector in complex space forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surfaces with parallel mean curvature vector in complex space forms will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-463666