From the reviews:" In this Lecture Note volume the author describes his differential-
geometric approach to parametrical statistical problems summarizing the results he had …

P. Wintgen proved in Sur l'inégalité de Chen-Willmore. CR Acad. Sci. Paris 288, 993–995
(1979) that the Gauss curvature G and the normal curvature K^D of a surface in the …

Abstract The theory of $\delta $-invariants, initiated by the author in the early 1990s, is a
challenging topic in modern differential geometry, having a lot of applications. In the spirit of …

Differential geometry provides an aesthetically appealing and oftenrevealing view of
statistical inference. Beginning with anelementary treatment of one-parameter statistical …

Beginning with the theory of curves and surfaces in ordinary Euclidean 3-space, the theory
of submanifolds as a subarea of differential geometry dates back as far as differential …

Several years ago our statistical friends and relations introduced us to the work of Amari and
Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen …

Geometrical foundations of asymptotic inference are described in simple cases, without the
machinery of differential geometry. A primary statistical goal is to provide a deeper …

Hypersurfaces in statistical manifolds - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue …

In this paper, we study the behaviour of submanifolds in statistical manifolds of constant
curvature. We investigate curvature properties of such submanifolds. Some inequalities for …

A statistical manifold is a smooth manifold equipped with a pair of a Riemannian metric and
a torsion-free affine connection satisfying the Codazzi equation. We naturally have various …