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Rank and k-nullity of contact manifolds
Article
Rukimbira, P. (2004). Rank and k-nullity of contact manifolds .
2004(20), 1025-1034. 10.1155/S0161171204309142
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Rukimbira, P. (2004). Rank and k-nullity of contact manifolds .
2004(20), 1025-1034. 10.1155/S0161171204309142
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cited authors
Rukimbira, P
authors
Rukimbira, Philippe
abstract
We prove that the dimension of the 1-nullity distribution N (1) on a closed Sasakian manifold M of rank I is at least equal to 21-1 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. Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.
publication date
December 1, 2004
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Digital Object Identifier (DOI)
https://doi.org/10.1155/s0161171204309142
Additional Document Info
start page
1025
end page
1034
volume
2004
issue
20