Curves and surfaces in a Euclidean space are approachable research topics. Numerous and in-depth studies on them are the century-old traditions of geometry, and at the very foundation of it. Differential geometry of submanifolds is a direct generalization of this research field. At present, I am particularly interested in two specific areas. One is geometry of submanifolds in a vector space, so-called centroaffine differential geometry. The other is geometry of statistical manifolds. It’s an important concept in information geometry, an emerging research domain, and is also closely related to affine differential geometry and Hessian geometry. Let’s enjoy exploring the world of forms and shapes together.
- Fujioka A., Furuhata H., and Sasaki T., Projective minimality for centroaffine minimal surfaces, J. Geom. 105(2014), 87-102.
- Furuhata H., Hypersurfaces in statistical manifolds, Differential Geom. Appl. 27(2009), 420–429.
- Furuhata H.and Vrancken, L., The center map of an affine immersion, Results Math. 49(2006), 201–217.