Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature - Aydin, M. Evren; Mihai, Adela; Mihai, Ion (World Scientific Publ Co Pte Ltd, 2017)
The Wintgen inequality (1979) is a sharp geometric inequality for surfaces in the 4-dimensional Euclidean space involving the Gauss curvature (intrinsic invariant) and the normal curvature and squared mean curvature (extrinsic invariants), respectively. De Smet et al. (Arch. Math. (Brno) 35:115-128, 1999) conjectured a generalized Wintgen inequality for submanifolds of arbitrary dimension and codimension in Riemannian space forms. This conjecture was proved by Lu (J. Funct. Anal. 261:1284-1308, 2011) and by Ge and Tang (Pac. J. Math. 237:87-95, 2008), independently. In the present paper we establish a generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature.
Keywords: Wintgen inequality; Statistical manifold; Statistical submanifold; Dual connections