Abstract
We consider statistical submanifolds in Sasaki-like statistical manifolds. We give some examples of invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds. We prove Chen-like inequality involving scalar curvature and Chen-Ricci inequality for these kinds of submanifolds.
Highlights
Statistical manifolds have arisen from the study of a statistical distribution
Statistical manifolds have many applications in information geometry, which is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory
We prove the Chen–Ricci inequality for statistical submanifolds in Sasaki-like statistical manifolds
Summary
Statistical manifolds have arisen from the study of a statistical distribution. In 1985 Amari [2] introduced a differential geometric approach for a statistical model of discrete probability distribution. Motivated by the studies of the above authors, in the present paper, we define invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds and give some examples of these submanifolds. (M, ∇, g, φ, ξ, η) is called a Sasaki-like statistical manifold and considered the curvature tensor R with respect to ∇ such that
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