My main research interests are in Differential Geometry. For the past decade I have been most interested in Lie sphere geometry applied to problems of Dupin hypersurfaces in spheres and isoparametric hypersurfaces, and to surfaces in space (that is, in three-dimensional space forms).
The following is a list of my papers. There are links to preprints (as ps or pdf files) which have not yet appeared in published form.
1. Homogeneous Einstein Spaces of Dimension Four, J. Diff. Geom. 3 (1969), pp. 309-349 (Dissertation).
2. The scalar curvature of left-invariant Riemannian metrics, Indiana University Math. J. 29 (1971), pp. 1125 - 1144.
3. Einstein metrics on principal fire bundles, J. Diff. Geom. 8 (1973), pp. 599 - 614.
4. Imbeddings of Stiefel manifolds into Grassmannians, Duke Math. J. 42 (1975), pp. 397 - 407.
5. Higher order contact of submanifolds of homogeneous spaces, Lecture Notes in Math. 610, Springer-Verlag, New Nork, 1977, 166 pages.
6. Deformation of submanifolds of homogeneous spaces, J. Diff. Geom. 16 (1981), pp. 213-246.
7. Projective deformation and biholomorphic equivalence of real hypersurfaces, Ann. Glo-bal Anal. and Geom. 1 (1983), pp. 1 - 34.
8. Second order projective deformation of real hypersurfaces, Tensor, N.S. 39 (1983), pp. 135 - 140.
9. Minimal surfaces in spheres by the method of moving frames, Revue de l'Insitute E. Cartan 12 (1988), Nancy, France (with M. Rigoli).
10. Minimal surfaces in spheres by the method of moving frames, Rend. Sem. Mat. Univers. Politec. Torino, Special Volume (1983), pp. 75 - 98 (with M. Rigoli).
11. A class of harmonic maps from surfaces into real Grassmannians, Rend. Sem. Mat. Univers. Politec. Torino, Special Volume (1983), pp. 99 - 116 (with M. Rigoli).
12. Quantization of curvature of harmonic two-spheres in CPn, preprint (1986), 41 pages, preliminary version of  (with M. Rigoli).
13. Differential systems and isometric embeddings, Annals of Math. Study 114, Princeton Universtiy Press, 1987, 225 pages (with P. Griffiths).
14. Holomorphic curves in the complex quadric, Bull. Australian Math. Soc. 35 (1987), pp. 125 - 147 (with M. Rigoli and K. Yang).
15. On conformal minimal immersions of S2 into C Pn, Math. Ann. 279 (1988), pp. 599-620, with J. Bolton, M. Rigoli and L. Woodward.
16. Harmonically immersed surfaces of Rn, Trans. Amer. Math. Soc. 307 (1988), pp. 363 - 372 (with M. Rigoli). Correction, Trans. Amer. Math. Soc. 311 (1989), pp. 425 - 428.
17. Harmonic maps, twistor spaces and twistor lifts, Fibre Bundles: Their Use in Physics, eds. J.T. Ezin and A. Verjovski, World Scientific Press, Singapore, 1988, pp. 11 - 22 (with M. Rigoli).
18. Harmonic Gauss maps, Pacific J. Math. 136 (1989), pp. 261 - 282 (with M. Rigoli).
19. On the isotropy of compact minimal surfaces in CPn, Math Z. 200 (1989), pp. 169 - 180 (with M. Rigoli).
20. Twistor and Gauss lifts of surfaces in four manifolds, Recent Developments in Geometry 101, eds. S.-Y. Cheng, H. Choi and R. Greene, Amer. Math. Soc., Providence, RI, 1989, pp. 197 - 232 (with M. Rigoli).
21. Review of Einstein Manifolds by A. Besse, Springer - Verlag, 1987, Bull. Amer. Math. Soc. 20 (1989), pp. 142 - 145.
22. Neutral surfaces in neutral four-manifolds, Le Matematiche 45 (1990), pp. 407 - 443 (with M. Rigoli). Reprint
23. Einstein metrics on circle bundles, Proc. Symposia in Pure Math. 54 (1993), Part 2, pp. 331 - 336 (with M. Rigoli).
24. Rigidity of hypersurfaces in complex projective space, Ann. Sci. Ecole Norm. Sup. 27 (1994), pp. 227 - 248 (with E. Musso).
25. Families of flat minimal tori in CPn, J. Diff. Geom. 42 (1995), pp. 113-132 (with R. Liao).
26. Isoparametric functions and flat minimal tori in CP2, Proc. Amer. Math. Soc 123 (1995), pp. 2849-2854 (with Q-S. Chi and R. Liao).
27. Dupin hypersurfaces, Geometry and Topology of Submanifolds, VII, eds. F. Dillen et al., World Scientific, River Edge, New Jersey, 1995, pp. 100 - 105 (with T. Cecil).
28. Irreducible Dupin hypersurfaces with three principal curvatures, Inventiones Mathematicae 132 (1998) pp. 121-178 (with T. Cecil).
29. Jump-Diffusion Markov Processes on Orthogonal Groups for Object Pose Estimation, J. of Statistical Planning and Inference, 103, Issues:1-2 (2002) pp. 15-37 (with A. Srivastava, U. Grenander, & M.I. Miller).
30. Dupin hypersurfaces with four principal curvatures, Geometriae Dedicata 79 (2000) pp. 1-49 (with T. Cecil).
31. 150 Years of Mathematics at Washington University in St. Louis, Amer. Math. Soc., Contemporary Mathematics 395, (2006) (edited with S.G. Krantz).
32. Isoparametric hypersurfaces with four principal curvatures, Annals of Math, 166 (2007), pp. 1-76 (with T. Cecil and Q-S. Chi).Reprint
33. Dupin hypersurfaces with four principal curvatures, II, Geometriae Dedicata, 128 (2007), pp. 55-95 (with T. Cecil and Q-S. Chi).
34. Classifications of Dupin Hypersurfaces, in F. Dillen and I. Van de Woestyne, eds., Pure and Applied Differential Geometry, PADGE 2007, Shaker Verlag, Aachen, (2007), 48-56 (with T. Cecil and Q.-S. Chi).
35. On Kuiper's question whether taut submanifolds are algebraic, Pac. J. of Math. 234 (2008), No. 2, pp. 229-247 (with Q.-S. Chi and T. Cecil). Reprint