International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 20, Pages 1025-1034

Rank and k-nullity of contact manifolds

Philippe Rukimbira

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.


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 2l1 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.