Recent Publications for Thomas E. Cecil


Books

  1. Tight and Taut Immersions of Manifolds (with P.J. Ryan), Research Notes in Mathematics 107, Pitman, London, 1985
  2. Lie Sphere Geometry, Springer Verlag, New York, 1992.
  3. Tight and Taut Submanifolds (T. Cecil and S.-S. Chern, eds.) MSRI Publications 32, Cambridge University Press, 1997.
  4. Lie Sphere Geometry, With Applications to Submanifolds, 2nd Edition, Springer Verlag, New York, 2008.
  5. 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.
  6. Geometry of Hypersurfaces, (with P.J. Ryan), Springer Monographs in Mathematics, Springer, New York et al., 2015.

Recent Articles

  1. Focal Points and Support Functions in Affine Differential Geometry, Geometriae Dedicata 50 (1994), 291-300.
  2. An Affine Characterization of the Veronese Surface (with M. Magid, L. Vrancken), Geometriae Dedicata 57 (1995), 55-71.
  3. Dupin Hypersurfaces (with G. Jensen) Geometry and Topology of Submanifolds VII, 100-107, World Scientific, River Edge, NJ, 1995.
  4. Taut and Dupin Submanifolds, Tight and Taut Submanifolds, MSRI Publications 32, 135-180, Cambridge University Press, 1997.
  5. Dupin Hypersurfaces with Three Principal Curvatures (with G. Jensen), Inventiones Mathematicae 132 (1998), 121-178.
  6. Dupin Hypersurfaces with Four Principal Curvatures (with G. Jensen), Geometriae Dedicata 79 (2000), 1-49.
  7. Isoparametric Hypersurfaces with Four Principal Curvatures (with Q.-S. Chi and G. Jensen), Annals of Math 166 (2007), 1-76.
  8. Dupin Hypersurfaces with Four Principal Curvatures II (with Q.-S. Chi and G. Jensen), Geometriae Dedicata 128 (2007), 55-95.
  9. 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.
  10. On Kuiper's Question Whether Taut Submanifolds are Algebraic (with Q.-S. Chi and G. Jensen), Pacific J. Math 234, (2008), 229-248.
  11. Isoparametric and Dupin Hypersurfaces, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 4 (2008), 062, 28 pages.
  12. Compact Dupin Hypersurfaces, Notices ICCM, 9 (2021), Number 1, 57-68, DOI: https://dx.doi.org/10.4310/ICCM.2021.v9.n1.a4
  13. Using Lie Sphere Geometry to Study Dupin Hypersurfaces in Rn, Axioms, 2024, 13, 399. https://doi.org/10.3390/axioms13060399
  14. Classifications of Dupin Hypersurfaces in Lie Sphere Geometry, Acta Mathematica Scientia, 2024, 44: 1-36, https://doi.org/10.1007/s10473-024-0101-7

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