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The first part of this paper is concerned with geometrical and cohomological properties of Lie flows on compact manifolds. Relations between these properties and the Euler class of the flow are given.
The second part deals with 3-codimensional Lie flows. Using the classification of 3-dimensional Lie algebras we give cohomological obstructions for a compact manifold admits a Lie flow transversely modeled on a given Lie algebra.
We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide also a Gauss-Bonnet theorem for a special class of evolutes.
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