Extremities for statistical submanifolds in Кenmotsu statistical manifolds

Abstract

Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. It has been shown that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold by constructing a counter-example. Finally, we prove a very well-known Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds of constant ?-sectional curvature by adopting optimization techniques on submanifolds. This article ends with some concluding remarks.

Statistical Solitonic Impact on Submanifolds of Kenmotsu Statistical Manifolds

“…The study of the Kenmotsu manifold is an important part of contact geometry in differential geometry, with important applications in theoretical physics, among other areas. Its statistical equivalent, the Kenmotsu statistical manifold (see [34]), is also significant and is as important as the original Kenmotsu manifold. The interest from theoretical physicists has extended towards equations involving Ricci solitons and Yamabe solitons, particularly in the context of Einstein manifolds, quasi-Einstein manifolds, and string theory.…”

Distributions in CR-lightlike submanifolds of an indefinite Kaehler statistical manifold

“…Statistical manifolds, which are geometrically formulated as Riemannian manifolds with a certain affine connection were introduced by [12] and afterwards explored by [2], [7], [1], et.al., where they studied the probability information from the perspective of differential geometry. Henceforth, the notion of statistical counterpart of the Kenmotsu manifold, that is, Kenmotsu statistical manifold was initiated by [9] and subseqently researched by [6], [3], [13] et.al. for its geometrical properties and statistical curvature.…”