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Publications of Robert Gardner

  1. Thesis : " Differential Geometric Methods in Partial Differential Equations " , Berkeley University Press, 150 pages, 1965.
  2. "Invariants of Pfaffian systems", Trans. Amer. Math. Soc. 126 (1967), 514-533.
  3. " Some Applications of the Retraction Theorem in Exterior Algebra ", J. Diff. Geom. 2 (1968), 25-31.
  4. "The Cauchy Problem for Pfaffian Systems ", Comm. Pure and App. Math. 22 (1969), 587-596.
  5. " A Differential Geometric Generalization of Characteristics ", Comm. Pure and App. Math. 22 (1969), 597-626.
  6. " An Integral Formula for Immersions in Euclidean Space ", J. Diff. Geom. 3 (1969), 245-252.
  7. " The Dirichlet Integral in Differential Geometry ", Proc. Symposia in Pure Math. vol. 15, Amer. Math. Soc. Providence (1970), 231-238.
  8. " A Differential Geometric Approach to Characteristics ", Proc. Symposia in Pure Math. vol. 16, Amer. Math. Soc. Providence (1970), 179-186.
  9. " The Technique of Integral Formulas in the Geometry of Immersiions ", Mathematisches Forschungsinstitut Oberwolfach Berichte 4 (1971).
  10. " The Geometry of Subscalar Pairs of Metrics ", Proc. Carolina Conference on Minimal Surfaces and Several Complex Variables (1971), 29-42.
  11. " Subscalar Pairs of Metrics and Hypersurfaces with a Nondegenerate Second Fundamental Form ", J. Diff. geom. 6 (1972), 437-458.
  12. " Lectures on Exterior Algebras over Commutative Rings ", UNC Lecture Notes (1972).
  13. " The Influence of Caratheodory on Differential Systems ", C. Caratheodory Symposium, Greek Mathematics Society (1973), 146-153.
  14. " Geometry of Submanifolds of Rn ", Proc. Symp.Pure Math. , vol. 27, Amer. Math. Soc. Providence (1975), 125-134.
  15. " The Fundamental Theorem of Vector Relative Invariants ", Jour. Algebra 36 (1975), 314-318.
  16. " Modules which Admit Determinants ", J. Linear and Multilinear Algebra 3 (1975), 209-214.
  17. " New Viewpoints in the Geometry of Submanifolds in Rn ", Bull. Amer. Math. Soc. 83 (1977), 1-35.
  18. " Differential Geometric Viewpoints on the Developments of Shockwaves ", in the 1976 Ames Research Center (NASA) Conference on the Geometric Theory of Nonlinear Waves, editor Robert Herman, vol. 6, Math-Science Press (1977), 89-104.
  19. " Differential Geometry and Foliations " in Differential Foliations and Gelfand-Fuks Cohomology, edited Paul Schweitzer, Springer Lecture notes in Math., vol.652 (1978), 75-94.
  20. " Constructing Backlund Transformations ", in Partial Differential Equations and Geometry, edited C. Byrnes, Marcel Dekker, (1979), 77-87.
  21. " Invariant Theory ", Bull. Amer. Math. Soc. 12 (1980), 246-256.
  22. " Exterior Differential Systems ", (joint with R. Bryant, S.S. Chern and P. Griffiths), China Scientific Press, publication no. 3.
  23. " Differential Geometric Methods Interfacing Control Theory ", in Diff. Geom Control Theory, vol. 27, Progress in Math., Birkhauser (1983), 117-180.
  24. " Equivalence of 1-dim. Lagrangian Field Theories in the plane I ", (joint with W. Shadwick), Springer Lecture Notes in Math. vol. 1156 (1985), 154-179.
  25. " A Simple Characterization of the Contact System on Jk(E) ", (joint with W. Shadwick), Rocky Mountain J. Math. 17(1987), 19-21.
  26. " Differential Equations and the Method of Equivalence ", Proc. IEEE Conference on Decision and Control, Fort Lauderdale, Fla. Dec. 1985, 1777-1778.
  27. " Overdetermined Equivalence Problems with an Application to Feedback Equivalence ", (joint with W. Shadwick), Proc. San Antonio Conf. on Diff. Geom., Contemporary Mathematics, Amer. Math. Soc., 111-120.
  28. " Feedback Equivalence of Control Systems ", (joint with W. Shadwick), Systems and Control Letters 8 (1987), 463-465.
  29. " The Principal Components Construction Applied to Affine Unimodular Repere Mobile ", Results in Mathematics 13 (1988), 235-239.
  30. " A Geometric Isomorphism with Applications to Closed Loop Controls ", (joint with W. Shadwick and G. Wilkens), SIAM Journal of Control 27 (1989), 1361-1368.
  31. " Feedback Equivalence and Symmetries of Brunowski Normal Forms ", (joint with W. Shadwick and G. Wilkens), Contemporary Mathematics, vol 97, Amer. Math. Soc., Providence 1989,115-130.
  32. " The Method of Equivalence and its Applications ", SIAM-CBMS Regional Conference Series in Applied Mathematics, vol. 58, 1989, 127 pages.
  33. " The Geometry of Nonlinear Control Systems ", in Differential Geometry, a Symposium in honor of Manfredo do Carmo, Pitman Monogrpahs and Surveys in Pure and Applied Mathematics, vol. 51 (1991), 179-198.
  34. " Feedback Equivalence for General Control Systems ", (joint with W. Shadwick), Systems and Control Letters 15 (1990), 15-23.
  35. " Exterior Differential Systems ", (joint with R. Bryant, S.S. Chern, P. Griffiths and H. Goldschmidt), MSRI Pub. # 18, Springer, 1990, 525 pages.
  36. " An Algorithm for Feedback Linearization ", (joint with W. Shadwick), Diff. Geom. and its Apps. vol.1, no.2 (1991), 153-158.
  37. " Image Segmentation and Evaluation of Deformation Features ", (joint with Oliver, Pizer and Pryzwansky).
  38. " Symmetry and the Implementation of Feedback Linearization ", (joint with W. Shadwick), Systems and Control Letters 15 (1990), 25-33.
  39. " An Equivalence Problem for a 2-Form and a Vector Field in R3 ", (joint with W. Shadwick), CMS Proc. 12, Differential Geometry, Global Analysis and Topology (1992), 41-50.
  40. " Evaluation of Cytological Deformation by Boundary Driven Energy Minimization ", (joint with Oliver, Pizer and Pryzwansky), in Information Processing in Medical Imaging, Wiley-Liss, NY, vol. 363 (1991), 355-358.
  41. " Characteristics and the Geometry of Hyperbolic Equations in the Plane ", (joint with N. Kamran), Jour. Diff. Equations., 104 (1993),60-116.
  42. " Classical geometries arising in feedback equivalence ", Proceedings of the 32nd IEEE Conference on Decision and Control,(1993),3437-3440.
  43. " The GS-algorithm for Exact Linearization to Brunovsky Normal Form ", (joint with W. Shadwick), IEEE Transactions on Automated Control, 37 (2) (1992), 224-230.
  44. " Ridges for Image Analysis ", (joint with D. Eberly,B. Mardo and S. Pizer), Journal of Math Imaging and Vision, 4 (1994), 353-373.
  45. " Generalized Spherical Functions on Projectively Flat Manifolds ", Results in Math. 27 (1995), 41-50.
  46. " Control Structures ", (joint with R. Bryant), Banach Center Publ. # 32, Warsaw, (1995), 111-121.
  47. " Normal forms and focal systems for determined systems of two first-order partial differential equations in the plane ", (joint with N. Kamran),Indiana Univ. Math. J. 44 (4)(1995), 1127-1162

  48. " Applications of Finsler Geometry to Control Theory " (preface), (joint with G. Wilkens), Proc. of the conference Finsler Geometry,Seattle 1995, in Contemp. Math. 196, Amer. Math. Soc., Providence, 1996, pages 227-229.

  49. " A Pseudogroup Isomorphism between Control Systems and Certain Generalized Finsler Structures ", (joint with G. Wilkens), Proc. of the conference Finsler Geometry, Seattle 1995, in Contemp. Math. 196, Amer. Math. Soc., Providence, 1996, page s 231-243.

  50. " The Fundamental Theorems of Curves and Hypersurfaces in Centro-affine Geometry", (joint with George Wilkens), Bull. Belgian Math. Soc. Simon Stevin 4 (3) (1997),379-401.

  51. " Exterior Differential Systems and Normal Forms of Parabolic Systems ", (joint with N. Kamran),in Advances in Mathematical Sciences : CRM's 25 Years, Montreal, PQ 1994,CRM Proc. Lecture Notes 11, Amer. Math. Soc., Providence 1996,215-230.