Preprints

  1. On the geometry of the cross-cap in the Minkoswki 3-space. (With F.S. Dias) Submitted 2012 pdf file

  2. On the geometry of singular surfaces. (With R. Oset Sinha) Submitted, 2012. Pdf file

Publications

  1. Apparent contours in Minkowski 3-space and first order ordinary differential equations. (With S. Izumiya) To appear in Nonlinearity pdf file

  2. Umbilics of surfaces in the Minkowski 3-space. To appear in J. Math. Soc. Japan. Pdf file

  3. Projections of space curves and duality. To appear in Q. J. Math. doi:10.1093/qmath/har035 (With R. Oset Sinha) pdf file

  4. Curves in the Minkowski plane and their contact with pseudo-circles. Geometria Dedicata, 159 (2012), 109--124. doi: 10.1007/s10711-011-9649-1. (With A. Saloom) pdf file

  5. A note on binary quintic forms and lines of principal curvature on surfaces in R5. Topology and its Applications, 159 (2012), 562-567. doi:10.1016/j.topol.2011.09.032. (With M. A. S. Ruas) pdf file

  6. Caustics of surfaces in the Minkowski 3-space. Q. J. Math. 63 (2012), 189-209. doi: 10.1093/qmath.laq030. Pdf file

  7. Families of curve congruence on Lorentzian surfaces and pencils of quadratic forms. Proc. Roy. Soc. Edinburgh Sect. A. 141A (2011), 655--672. (With A. C. Nabarro) pdf file

  8. Projections of timelike surfaces in the de Sitter space. Real and Complex Singularities. Edited by M. Manoel, M. C. Romero Fuster, C. T. C. Wall. London Mathematical Society Lecture Notes Series (No. 380), 2010. (With S. Izumiya) pdf file

  9. Pairs of foliations on surfaces. Real and Complex Singularities. Edited by M. Manoel, M. C. Romero Fuster, C. T. C. Wall. London Mathematical Society Lecture Notes Series (No. 380), 2010. pdf file

  10. Folding maps on spacelike and timelike surfaces and duality. Osaka J. Math. 47 (2010), 839--862. (With S. Izumiya and M. Takahashi) pdf file

  11. Families of Gauss indicatrices on smooth surfaces in pseudo-spheres in the Minkowski 4-space. Journal of Singularities, 1 (2010), 116-133. Available from http://www.journalofsing.org/volume1/article8.html

  12. Self-adjoint operators on surfaces with singular metrics. J. Dyn. Control Syst. 16 (2010), 329--353. (With S. Izumiya) pdf file

  13. Projections of surfaces in the hyperbolic space along horocycles. Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 399-418. (With S. Izumiya) pdf file

  14. Families of surfaces and conjugate curve congruences. Advances in Geometry, 9 (2009), 279-309. (With A. C. Nabarro) pdf file

  15. Self-adjoint operators on surfaces in Rn. Differential Geometry and its Applications, 27 (2009), 296-306. Pdf file

  16. Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes. Rev. Mat. Iberoamericana 24 (2008), 895-920. (With S. Izumiya) pdf file

  17. Vector fields tangent to foliations. Proc. Edinburgh Math. Soc 51 (2008), 765--778. (With L. F. Martins) pdf file

  18. Two-parameter families of binary differential equations. Discrete Contin. Dynam. Systems, 22 (2008), 759-789. pdf file

  19. On pairs of regular foliations in R3 and singularities of map-germs. Geometria Dedicata 135 (2008), 103-118. (With L. F. Martins and R. D. S. Oliveira) pdf file

  20. Asymptotic curves on surfaces in R5. Communications in Contemporary Mathematics, 10 (2008), 309--335. (With M. C. Romero-Fuster and M. A. S. Ruas) pdf file

  21. Surfaces in R4 and their projections to 3-spaces. Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 1313--1328. (With J. J. Nuno-Ballesteros) pdf file

  22. On pairs of geometric foliations on a cross-cap. Tohoku Math. J. 59 (2007), 233--258.

  23. Geometric properties of the solutions of implicit differential equations. Discrete Contin. Dynam. Systems 17 (2007), 349--364.

  24. Two-parameter families of implicit differential equations. Discrete Contin. Dynam. Systems 13 (2005), 139--262.

  25. Dupin indicatrices and families of curve congruences. Trans. Amer. Math. Soc. 357 (2005), 267--285. (With J. W. Bruce)

  26. On families of square matrices. Proc. London Math. Soc. 89 (2004), 738--762. (With J. W. Bruce)

  27. Zero curves of families of curve congruences. Real and Complex Singularities (Sao Carlos, 2002), Ed. T. Gaffney and M. Ruas, Contemp. Math., 354, Amer. Math. Soc., Providence, RI, June 2004. (With J. W. Bruce and G. J. Fletcher)

  28. On pairs of regular foliations in the plane. Hokkaido Math. J. 31 (2002), no. 3, 523--537. (With R. D. S. Oliveira)

  29. Families of surfaces in R4. Proc. Edinb. Math. Soc. (2) 45 (2002), 181--203. (With J. W. Bruce)

  30. On differential 1-forms in the plane. Discrete Contin. Dynam. Systems 6 (2000), no. 3, 519--536. (With R. D. S. Oliveira)

  31. Duality and implicit differential equations. Nonlinearity 13 (2000), 791--812. (With J. W. Bruce)

  32. Bifurcations of binary differential equations. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 485--506. (With J. W. Bruce and G. J. Fletcher)

  33. Real and Complex Singularities, J.W. Bruce and F. Tari (Editors), Proceedings of the 5th Workshop on Real and Complex Singularities, 27-31 July 1998, Sao Carlos, Brazil. CRC Research Notes in Mathematics 412, Chapman & Hall/CRC, 2000.

  34. Families of surfaces: focal sets, ridges and umbilics. Math. Proc. Cambridge Philos. Soc. 125 (1999), 243--268. (With J.W. Bruce and P. J. Giblin)

  35. Families of surfaces: height functions and projections to plane. Math. Scand. 82 (1998), 165--185. (With J.W. Bruce and P. J. Giblin)

  36. On the multiplicity of implicit differential equations. J. Differential Equations 148 (1998), 122-147. (With J. W. Bruce)

  37. Generic 1-parameter families of binary differential equations. Discrete Contin. Dynam. Systems 3 (1997), 79--90. (With J. W. Bruce)

  38. Implicit differential equations from singularity theory viewpoint. Singularities and differential equations (Warsaw, 1993), 23-38, Banach Center Publ., 33, Polish Acad. Sci., Warsaw, 1996. (With J. W. Bruce)

  39. Extrema of principal curvature and symmetry. Proc. Edinburgh Math. Soc. 39 (1996), 397--402. (With J. W. Bruce)

  40. On the geometry of simple germs of corank 1 maps from R3 to R3. Proc. Camb. Phil. Soc. 119 (1996), 469--481. (With W. L. Marar)

  41. Ridges, Crests and Sub-parabolic lines of evolving surfaces. Int. J. Computer Vision 18 (1996), 195--210. (With J. W. Bruce and P. J. Giblin)

  42. Parabolic curves of evolving surfaces. Int. J. Computer Vision 17 (1996), 291--306. (With J. W. Bruce and P. J. Giblin)

  43. Families of surfaces: height functions, Gauss maps and duals. In W.L. Marar (Ed.), Real and Complex Singularities, Pitman Research Notes in Mathematics 333 (1995), 148--178. (With J.W. Bruce and P. J. Giblin)

  44. On binary differential equations. Nonlinearity 8 (1995), 255--271. (With J. W. Bruce)

  45. Perpendicular bisectors, duals and local symmetry in the plane. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), 181--194. (With P. J. Giblin)

  46. Recognition of K-singularities of functions. Experimental Mathematics 1 (1992), no. 3, 225--229.

  47. Local reflexional and rotational symmetry in the plane. Springer Lecture Notes in Mathematics 1462 (1991), 154--171. (With P. J. Giblin)

  48. Projections of piecewise-smooth surfaces. J. London Math. Soc. 44 (1991), 155--172.

Last updated: 30 January, 2013.