On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection

Abstract

This research deals with the generalized symmetric metric U-connection defined on golden Lorentzian manifolds. We also derive sharp geometric inequalities that involve generalized normalized δ-Casorati curvatures for submanifolds of golden Lorentzian manifolds equipped with generalized symmetric metric U-connection.

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

“…Thus, thanks to ( 41) and ( 42), one obtains the equality sign in (33) if and only if the submanifold ℵ is invariantly quasi-umbilical with a trivial normal connection in Θ. Therefore, with respect to suitable local orthonormal normal and orthonormal tangent a frames, the shape operators satisfy (35).…”

“…Therefore, (33) easily holds in the light of the above equation. In addition, a sign of the equality holds in (33) if and only if…”

“…Lee et al [32] established a Casorati Curvature for the submanifolds in generalized space forms endowed with semi-symmetric metric connections and Kenmotso space forms. Majid et al [33] also derived sharp geometric inequalities that involve generalized normalized δ-Casorati Curvatures for submanifolds of golden Lorentzian manifolds equipped with generalized symmetric metric U-connection.…”

Inequalities for the Generalized Normalized δ-Casorati Curvatures of Submanifolds in Golden Riemannian Manifolds

“…Using the Chen invariants and the mean curvature, the primary extrinsic invariant for Riemannian submanifolds, he established sharp inequality relations that are known as Chen inequalities. Chen invariants and Chen inequalities for various submanifolds in different ambient spaces have been intensively investigated (see [10][11][12][13][14][15][16][17], etc. ).…”

Almost Bronze Structures on Differentiable Manifolds

“…ese structures have been recently studied by many authors (see [1][2][3][4][5][6][7][8][9][10][11][12]). e term "metallic ratio" has been de ned by Spinadel [13] as a generalized form of the golden proposition in 1999 and coined the concept of the "metallic means family" or "metallic propositions."…”