On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection

Majid Ali Choudhary,Khaled Mohamed Khedher,Oğuzhan Bahadır,Mohd Danish Siddiqi

doi:10.3390/math9192430

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.

Highlights

Golden ratios have been investigated by different researchers for many centuries
Taking inspiration from golden mean, the golden structure introduced by [1] as a polynomial structure [2,3] came into picture, and the structure polynomial was written as φ2 = φ + I, φ being (1, 1) tensor field
In 2007, the authors in [4] investigated invariant submanifolds isometrically immersed in golden Riemannian manifolds, highlighting new ideas

Summary

Background

Golden ratios have been investigated by different researchers for many centuries. Taking inspiration from golden mean, the golden structure introduced by [1] as a polynomial structure [2,3] came into picture, and the structure polynomial was written as φ2 = φ + I, φ being (1, 1) tensor field. In 2007, the authors in [4] investigated invariant submanifolds isometrically immersed in golden Riemannian manifolds, highlighting new ideas. Bahadir and Sirajuddin et al [6] studied slant submanifolds in golden Riemannian manifolds, developing different useful results. Y. Chen established a relation in the form of an optimal inequality and defined and studied a new concept known as ideal immersion. Chen established a relation in the form of an optimal inequality and defined and studied a new concept known as ideal immersion This investigation of Chen’s invariants have been extensively used by many researchers in different ambient spaces ([13,14,15], etc.). We study the lower bounds for submanifolds immersed in golden Lorentzian manifolds equipped with generalized symmetric metric U-connection.

Preliminaries

Some Consequences

Discussion