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Trajectories on real hypersurfaces of type (A2) which can be seen as circles in a complex hyperbolic space


Abstract


We study trajectories for Sasakian magnetic fields on homogeneous tubes around totally geodesic complex submanifolds in a complex hyperbolic space. We give conditions that they can be seen as circles in a complex hyperbolic space, and show how the set of their congruence classes are contained in the set of those of circles. In view of geodesic curvatures and complex torsions of circles obtained as extrinsic shapes of trajectories, we characterize these tubes among real hypersurfaces in a complex hyperbolic space.

DOI Code: 10.1285/i15900932v37suppl1p19

Keywords: Sasakian magnetic fields; extrinsic circular trajectories; moduli space of circles; real hypersurfaces of type (A2); complex hyperbolic spaces

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