Recent Publications for Thomas E. Cecil
Books
- Tight and Taut Immersions of Manifolds (with P.J. Ryan), Research
Notes in Mathematics 107, Pitman, London, 1985
- Lie Sphere Geometry, Springer Verlag, New York, 1992.
- Tight and Taut Submanifolds (T. Cecil and S.-S. Chern, eds.)
MSRI Publications 32, Cambridge University Press, 1997.
- Lie Sphere Geometry, With Applications to Submanifolds, 2^{nd} Edition, Springer Verlag, New York, 2008.
- Lie Sphere Geometry and Dupin Hypersurfaces, Escola de Altos Estudos/Capes, Instituto de Mathematica e Estatistica, Universidade de Sao Paulo, Brazil, Short-course Notes, 101 pages, January 9-20, 2012.
- Geometry of Hypersurfaces, (with P.J. Ryan), Springer Monographs in Mathematics, Springer, New York et al., 2015.
Recent Articles
- Focal Points and Support Functions in Affine Differential Geometry,
Geometriae Dedicata 50 (1994), 291-300.
- An Affine Characterization of the Veronese Surface
(with M. Magid, L. Vrancken), Geometriae Dedicata 57 (1995), 55-71.
- Dupin Hypersurfaces (with G. Jensen) Geometry and Topology
of Submanifolds VII, 100-107, World Scientific, River Edge, NJ, 1995.
- Taut and Dupin Submanifolds, Tight and Taut Submanifolds, MSRI
Publications 32, 135-180, Cambridge University Press, 1997.
- Dupin Hypersurfaces with Three Principal Curvatures (with
G. Jensen), Inventiones Mathematicae 132 (1998), 121-178.
- Dupin Hypersurfaces with Four Principal Curvatures (with G. Jensen),
Geometriae Dedicata 79 (2000), 1-49.
- Isoparametric Hypersurfaces with Four Principal Curvatures
(with Q.-S. Chi and G. Jensen), Annals of Math 166 (2007), 1-76.
- Dupin Hypersurfaces with Four Principal Curvatures II
(with Q.-S. Chi and G. Jensen), Geometriae Dedicata 128 (2007), 55-95.
- Classifications of Dupin Hypersurfaces,
(with Q.-S. Chi and G. Jensen), Pure and Applied Differential Geometry,
PADGE 2007, F. Dillen and I. Van de Woestyne, editors, pp. 48-56,
Shaker Verlag, Aachen, 2007.
- On Kuiper's Question Whether Taut Submanifolds are Algebraic
(with Q.-S. Chi and G. Jensen), Pacific J. Math 234, (2008), 229-248.
- Isoparametric and Dupin Hypersurfaces, Symmetry, Integrability
and Geometry: Methods and Applications (SIGMA) 4 (2008), 062, 28 pages.
- Dupin Submanifolds in Lie Sphere Geometry (updated version)
(with S.-S. Chern), arXiv:2010.06429v1 [math.DG] 13 Oct 2020.
- Notes on Lie Sphere Geometry and the Cyclides of Dupin,
arXiv:2011.11432v1 [math.DG] 20 Nov 2020.
- Compact Dupin Hypersurfaces,
arXiv:2101.05316v2 [math.DG] 13 Apr 2021.
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Last Modified: 22 January 2016