The Structure on a Subspace of a Space with an f (an,an-1 ,an-2 ,....a2 ,a1)Structure

Abstract

Let
n
M be an almost contact manifold with an
f (an , an1, an2 , ......a2 , a1) structure of rank r and let
n 1
N

be
a hypersurface in
n
M . The following theorem is proved: if the
dimension of
1 1
( ( ))
n n
T N f TN
 
 is constant say s , for all
n 1
p N

 possesses a natural f (an , an1, an2 , ......a2 , a1)
structure of rank s . It is also proved that the naturally
induced f (an , an1, an2 , ......a2 , a1) structure is integrable if the
structure on
n
M is integrable and if the transversal to
n 1
N

can
be found to lie in the distribution
n
M .