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The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres.

NSF Award Search: Award# - Applications of Lie Sphere Geometry to Submanifold Theory

Of particular interest are isoparametric, Dupin and taut submanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants.

Spherical and elliptic geometries: an introduction - Universal Hyperbolic Geometry 33

The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods. Back to results. University of Bath Library. University of Bristol Libraries.


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Lie Sphere Geometry: With Applications to Submanifolds

Show next edition. Buy eBook. FAQ Policy. About this book Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space.

Lie Sphere Geometry