ArXiv versions are available for most of the articles listed below (see also the ADS listing).

*Conelike radiant structures*. [arXiv:2106.04270].

*Einstein equations for a metric coupled to a trace-free symmetric tensor*. [arXiv:2105.05514]. (A heavily revised version will be posted soon.)

*Commutative algebras with nondegenerate invariant trace form and trace-free multiplication endomorphisms*. [arXiv:2004.12343].

*Killing metrized commutative nonassociative algebras associated with Steiner triple systems*. Journal of Algebra, Vol. 608, No. 15 (October 2022), pp. 186-213. [arXiv:2205.08838].

*The commutative nonassociative algebra of metric curvature tensors*. Forum of Mathematics, Sigma 9 (2021), e79. [arXiv:1901.04012].

*Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form*. Analysis and Mathematical Physics 11, 43 (2021). [arXiv:1905.00071]. A correction to this article indicates how to fix the fallacious proof of Lemma 6.14. (The arxiv version incorporates the correction into the text.)

*Critical symplectic connections on surfaces*. Journal of Symplectic Geometry. Vol. 17, No. 6 (2019), pp. 1683-1771. [pdf][arXiv:1410.1468].

*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].

*Symmetries of the space of linear symplectic connections*. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 13 (2017), 002, 30 pages.

*Remarks on symplectic sectional curvature*. Differential Geometry and its Applications. Vol. 50 (February 2017), pp. 52-70. [arXiv:1610.05898].

*Infinitesimal affine automorphisms of symplectic connections*. Journal of Geometry and Physics. Vol. 106 (2016), pp. 210-212. [arXiv:1511.09258].

*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].

*Functions dividing their Hessian determinants and affine spheres*. The Asian Journal of Mathematics. Vol. 20, No. 3 (2016), pp. 503-530. [pdf] [arXiv:1307.5394].

*A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone*. Annali di Matematica Pura ed Applicata. Vol. 194, Issue 1 (2015), pp. 1-42. [arXiv:1206.3176].

*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.

*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]

*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).

*Einstein-like geometric structures on surfaces*. Annali della Scuola Normale Superiore, Classe di Scienze Vol. XII, issue 3 (2013) 499-585. [arXiv:1011.5723].

*Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations*. [arXiv:0909.1897]. >

*Projectively invariant star products*. International Mathematics Research Papers 9 (2005), 461-510, 2005. [math.DG:0504596]. (An [erratum] clarifies some ambiguities in the exposition.)

*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.)

*Contact Schwarzian derivatives*. Nagoya Mathematical Journal 179 (2005), 163-187. [math.DG:0405369].

*Contact path geometries*. [math.DG:0508343]. (I hope someday to rewrite this article completely. The arXiv version contains some mostly inconsequential but potentially confusing misstatements.)