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0111 · Jul 200119922001200920172026
5 results for well-positioned

Total torsion of 3D lines of curvature is an integer multiple of 2π.

problem Understanding the total torsion of 3D lines of curvature in Riemannian manifolds.
method Analyzing the properties of well-positioned lines of curvature and using the total torsion theorem for spherical curves.
result The total torsion of a well-positioned line of curvature is an integer multiple of 2π.

Let M3M^3 be an oriented 3-manifold. We investigate when one of the fibers or a combination of fiber components, FbestF_{best}, of a \emph{harmonic} map f:M3S1f: M^3 \to S^1 with Morse-type singularities delivers the Thurston norm χ([Fbest])χ_-([F_{best}]) of its homology class [Fbest]H2(M3;Z)[F_{best}] \in H_2(M^3; \Z). In particular, for a map …

2001-07-24abs ↗pdf ↗