International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 20, Pages 1025-1034
doi:10.1155/S0161171204309142
Rank and k-nullity of contact manifolds
Department of Mathematics, Florida International University, Miami 33199, FL, USA
Received 19 September 2003
Copyright © 2004 Philippe Rukimbira. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that the dimension of the 1-nullity distribution N(1)
on a closed Sasakian manifold M of rank l is at least equal
to 2l−1 provided that M has an isolated closed
characteristic. The result is then used to provide some examples
of k-contact manifolds which are not Sasakian. On a closed,
2n+1-dimensional Sasakian manifold of positive bisectional
curvature, we show that either the dimension of N(1)
is less
than or equal to n+1 or N(1) is the entire tangent bundle
TM. In the latter case, the Sasakian manifold M is isometric
to a quotient of the Euclidean sphere under a finite group of
isometries. We also point out some interactions between
k-nullity, Weinstein conjecture, and minimal unit vector fields.