My work in differential geometry addresses problems in (1) calibrated geometries, (2) submanifolds of complex projective space, and (3) Finsler geometry.
Lines on hypersurfaces (w/ J.M. Landsberg), submitted 2008.
Calibrated embeddings in the associative and Cayley cases (w/ Sema Salur), submitted 2007.
Fubini-Griffiths-Harris rigidity and Lie algebra cohomology (w/ J.M. Landsberg), submitted 2007.
Fubini's theorem in codimension two (w/ J.M. Landsberg), accepted by Crelle 2007.
The adjoint variety of SL(C) is rigid at order three, Differential Geom. Appl., accepted 2007.
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, vol. 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.