Minimal Atlases of Closed Contact Manifolds
نویسندگان
چکیده
We study the minimal number C(M, ξ) of contact charts that one needs to cover a closed connected contact manifold (M, ξ). Our basic result is C(M, ξ) ≤ dimM + 1. We also compute C(M, ξ) for all closed connected contact 3-manifolds:
منابع مشابه
On K-contact Manifolds with Minimal Number of Closed Characteristics
We prove that closed simply connected K-contact manifolds with minimal number of closed characteristics are homeomorphic to odd-dimensional spheres.
متن کاملm at h . SG ] 1 3 M ay 2 00 6 MINIMAL ATLASES OF CLOSED SYMPLECTIC MANIFOLDS
We study the number of Darboux charts needed to cover a closed connected symplectic manifold (M, ω) and effectively estimate this number from below and from above in terms of the Lusternik–Schnirelmann category of M and the Gromov width of (M, ω).
متن کاملProblems around 3–manifolds
This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4–manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton–Perelman revolution. We give sets of problems based on the following themes; Minimal surfaces and hyperbolic geometry of 3–manifolds. In particular, how do minimal surfaces gi...
متن کاملNon existence of totally contact umbilical slant lightlike submanifolds of indefinite Sasakian manifolds
We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian space forms.
متن کاملRank and k-nullity of contact manifolds
We prove that the dimension of the 1-nullity distributionN(1) on a closed Sasakianmanifold M of rank l is at least equal to 2l−1 provided thatM has an isolated closed characteristic. The result is then used to provide some examples ofK-contact manifolds which are not Sasakian. On a closed, 2n+ 1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension o...
متن کامل