These structures are known as   central if they are invariant under orthogonal transformation around zero.
The Seifert Conjecture says that any smooth nonzero one of these struc- tures has at least one closed orbit; it's true for Hopf maps but false in general. The Poincaré-Hopf theorem states that if one of these structures on a manifold ful lls certain conditions, then its index is equal to the Euler characteristic of that manifold. These structures are known as   central if they are invariant under orthogonal transformation around zero. These structures can be de ned generally as sections of the tangent bundle of a di erentiable manifold. These structures can be used to represent  ow lines. For ten points, identify these structures, operations on which include divergence and curl.
The Seifert Conjecture says that any smooth nonzero one of these struc- tures has at least one closed orbit; it's true for Hopf maps but false in general.
vector fields