Open Access
Hypersurfaces in Statistical Manifolds
Hitoshi Furuhata
- Vol. 852, pp 1-15
TLDR
The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given in this article as a first step of the statistical submanifold theory.Abstract:
The condition for the curvature of a statistical manifold
to admit a kind of standard hypersurface is given
as a first step of the statistical submanifold theory.
A complex version of the notion of statistical structures
is also introduced.read more
Citations
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Journal ArticleDOI
Some inequalities on submanifolds in statistical manifolds of constant curvature
TL;DR: In this article, the behaviour of submanifolds in statistical manifolds of constant curvature was studied and the curvature properties of such sub-mansifolds with any codimension and hypersurface were established.
Book ChapterDOI
Submanifold Theory in Holomorphic Statistical Manifolds
Hitoshi Furuhata,Izumi Hasegawa +1 more
TL;DR: In this article, the sectional curvature of a holomorphic statistical manifold is defined, and it is shown that a Lagrangian submanifold is of constant sectionality if and only if the statistical shape operator and its dual operator commute.
Journal ArticleDOI
Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions
TL;DR: The concept of quaternionic Kahler-like statistical manifold is defined and its main properties are derived, extending in a new setting some previous results obtained by K. Takano concerning statistical manifolds endowed with almost complex and almost contact structures.
Journal ArticleDOI
A study of Wintgen like inequality for submanifolds in statistical warped product manifolds
Cengizhan Murathan,Bayram Şahin +1 more
TL;DR: In this article, the Wintgen inequality for statistical submanifolds of statistical warped product manifolds was obtained for statistical manifold and its sub-manifold subspaces.
Journal ArticleDOI
Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature
TL;DR: In this article, the generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature has been established, which is a conjecture that was proved independently by Ge and Tang.
References
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Journal ArticleDOI
Special complex manifolds
TL;DR: The notion of a special complex manifold was introduced in this article, which is a complex manifold (M,J) with a flat torsion-free connection ∇ such that ∇J is symmetric.
Journal ArticleDOI
Fundamental equations for statistical submanifolds with applications to the bartlett correction
TL;DR: In this article, a set of equations that describe relationships between invariant quantities on the submanifold and supermanifolds when the Riemannian connection is used is extended to statistical manifolds, manifolds on which a pair of dual connections is defined.