Adelina Manea:Mastrogiacomo Leafwise Cohomology on a Foliated Manifold, p.75-86

Abstract:

We define the leafwise 2-jet of a differential function on a Riemannian foliated manifold $M$. If $M$ is endowed with a linear connection $\nabla$ then we define the Mastrogiacomo cohomology group with respect to $\nabla$ for homogeneous leafwise 2-jets. This group is isomorphic with the 1-dimensional Cech cohomology group with coefficients in the sheaf of germs of differentiable functions on $M$ whose gradient is parallel with respect to the connections induced by $\nabla$ on the leaves.

Key Words: foliated manifold, leafwise, cohomology.

2000 Mathematics Subject Classification: Primary: 53C12.

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