My work in differential geometry addresses problems in
(1) calibrated geometries,
(2) submanifolds of complex projective space, and
(3) Finsler geometry.
Parallel calibrations and minimal submanifolds, submitted.
Existence of orthogonal coordinates, in preparation.
Lines on hypersurfaces (w/ J.M. Landsberg), submitted 2008.
Calibrated embeddings in the associative and Cayley cases (w/ Sema Salur), Asian J. Math., September 2009.
Fubini-Griffiths-Harris rigidity and Lie algebra cohomology (w/ J.M. Landsberg), submitted 2007.
Fubini's theorem in codimension two (w/ J.M. Landsberg), J. Reine Angew. Math., 631 (2009), 221--235.
The adjoint variety of SL(C) is rigid at order three, Differential Geom. Appl., 26 (2008) 683--696.
Geodesics in Randers spaces of constant curvature, Trans. AMS 359 (2007), no. 4, 1633--1651.
Ricci and flag curvatures in Finser geometry (w/ D. Bao), in A Sampler of Riemann-Finsler Geometry, MSRI Series 50 2004.
Zermelo navigation on Riemannian manifolds (w/ D. Bao & Z. Shen), J. Diff. Geom. 66 (2004) 391--449.
On Randers metrics of constant flag curvature (w/ D. Bao), Rep. Math. Phys. 51 (2003) 9--42.