Optimization on slant submanifolds of golden Riemannian manifolds using generalized normalized $$\delta $$-Casorati curvatures

Abstract

In the present paper, we derive optimal inequalities involving generalized normalized δ-Casorati curvatures for slant submanifolds in a golden Riemannian space form. We obtain these inequalities by analysing a suitable constrained extrememum problem on submanifold.

Recent developments in δ-Casorati curvature invariants

“…, ξ m such that with respect to this frame the shape operator satisfies (9.6). [50] derived similar results for invariant and antiinvariant submanifolds of locally product golden space forms. Since φ is a self-adjoint, after interchanging X by φX , we obtain from (11.2) that g(φX, φY ) = g(φ 2 X, Y ) = pg(X, φY ) + qg(X, Y ).…”

Optimal Inequalities on (α,β)-Type Almost Contact Manifold with the Schouten–Van Kampen Connection

“…In the early 90s, B. Y. Chen [1] opened a new era by studying the relationship between extrinsic and intrinsic invariants with the help of a sharp inequality and introduced a new tool known as δ-invariants (or Chen's invariants). This conception was used by many researchers who studied Chen-type inequalities and Chen invariants in different ambient spaces (for more information see [2][3][4][5]).…”

Some Basic Inequalities on (ϵ)-Para Sasakian Manifold

“…It is very interesting to investigate the link between intrinsic and extrinsic invariants with the help of sharp inequality involving δ-invariants. A number of scenarios have been applied to Chen's invariants since their invention in [1] (refer to [2][3][4][5][6][7], etc.). The study of optimal inequalities turned out to be more appealing to the geometers with the introduction of Casorati curvature due to F. Casorati [8], and this event provided them a new tool to derive optimal inequalities with Casorati curvatures.…”