PROJECT TITLE :
Maurer-Cartan Forms for Fields on Surfaces: Application to Heart Fiber Geometry
We study the area of 1st order models of sleek frame fields using the strategy of moving frames. By exploiting the Maurer-Cartan matrix of affiliation forms we have a tendency to develop geometrical embeddings for frame fields that lie on spherical, ellipsoidal and generalized helicoid surfaces. We style methods for optimizing association forms in local neighborhoods and apply these to a statistical analysis of heart fiber geometry, using diffusion magnetic resonance imaging. This application of moving frames corroborates and extends recent characterizations of muscle fiber orientation in the guts wall, but conjointly provides for a wealthy geometrical interpretation. In particular, we have a tendency to will now acquire direct local measurements of the variation of the helix and transverse angles, of fiber fanning and twisting, and of the curvatures of the heart wall in that these fibers lie.
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