Submanifolds of Sasakian Space Forms with Parallel Mean Curvature Vector Fields and Equal Wirtinger Angles
From NZJM
New Zealand Journal of Mathematics
Vol. 36, (2007), Pages 23-34
Guanghan Li
School of Mathematical Science
Peking University
Beijing 100871
P.R. CHINA
and
School of Mathematics and Computer Science
Hubei University
Wuhan 430062
P.R. CHINA
Abstract We study closed submanifolds M of
dimension 2n + 1, immersed into a (4n + 1) − dimensional Sasakian
space form 
with constant
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 Kahler geometry.
Keywords Sasakian space, parallel mean curvature, Wirtinger angle, invariant submanifold, slant
Classification (MSC2000) 53C40, 53C42, 53C55
