Publications

ArXiv versions are available for most of the articles listed below.
The reviews of my articles on MathSciNet.
The reviews I have written for MathSciNet.
 

  1. Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form. [arXiv:1905.00071].
  2. The commutative nonassociative algebra of metric curvature tensors. [arXiv:1901.04012].
  3. Critical symplectic connections on surfaces. Journal of Symplectic Geometry. Vol. 17, No. 6 (to appear 2019). [arXiv:1410.1468].
  4. Left symmetric algebras and homogeneous improper affine spheres. Annals of Global Analysis and Geometry. Vol. 53, No. 3 (April, 2018), pp. 405-443. [arXiv:1707.08896].
  5. Symmetries of the space of linear symplectic connections. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 13 (2017), 002, 30 pages.
  6. Remarks on symplectic sectional curvature. Differential Geometry and its Applications. Vol. 50 (February 2017), pp. 52-70. [arXiv:1610.05898].
  7. Infinitesimal affine automorphisms of symplectic connections. Journal of Geometry and Physics. Vol. 106 (2016), pp. 210-212. [arXiv:1511.09258].
  8. Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero. Mathematische Nachrichten 290 (2017), no. 2-3, 293-320. [arXiv:1503.09108].
  9. Functions dividing their Hessian determinants and affine spheres. The Asian Journal of Mathematics. Vol. 20, No. 3, pp. 503-530, July 2016. [pdf] [arXiv:1307.5394].
  10. A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone. Annali di Matematica Pura ed Applicata. February 2015, Vol. 194, Issue 1, pp. 1-42. [pdf]
  11. Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations. Extended Abstracts Fall 2013, Research Perspectives CRM Barcelona (Trends in Mathematics), 2015, Birkäuser Basel. pp. 15-19.
  12. Ricci flows on surfaces related to the Einstein Weyl and Abelian vortex equations. Glasgow Mathematical Journal. Vol. 56, Issue 03 (Sept., 2014), pp. 569-599. [pdf]
  13. WHAT IS … an affine sphere? Notices of the American Mathematical Society. March 2012, Vol. 59, Issue 3. A Chinese translation (pdf) of this article is available in Mathematical Advances in Translation Vol. 35 (2), pp. 181-184. (ISSN 1003-3092).
  14. Einstein-like geometric structures on surfaces. Annali della Scuola Normale Superiore, Classe di Scienze Vol. XII, issue 3 (2013) 499-585. [arXiv:1011.5723].
  15. Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations.
    [arXiv:0909.1897]
  16. Projectively invariant star products. International Mathematics Research Papers 9 (2005), 461-510, 2005. [math.DG:0504596]. (An [erratum] clarifies some ambiguities in the exposition.) 
  17. Contact projective structures. Indiana University Mathematics Journal 54 (2005), 1547–1598. [math.DG:0402332]. (Note: In the statement of Theorem B, the assumption that the ambient connection is homogeneous is omitted, although it is assumed in the proof, and is necessary for the uniqueness.)
  18. Contact Schwarzian derivatives. Nagoya Mathematical Journal 179 (2005), 163-187. [math.DG:0405369]
  19. Contact path geometries. [math.DG:0508343] (I intend someday to rewrite this article completely. The arXiv version contains some mostly inconsequential but potentially confusing misstatements.)