Affiliation:
1. Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia
2. Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman
3. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Abstract
This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference35 articles.
1. The golden algebraic equations;Stakhov;Chaos Solitons Fractals,2006
2. Categorization of fractal plants;Chandra;Chaos Solitons Fractals,2009
3. Metallic structures on Riemannian manifolds;Hretcanu;Rev. Un. Mat. Argent.,2013
4. The metallic means family and multifractal spectra;Nonlinear Anal.,1999
5. On the curvature of the tangent bundle;Davis;Ann. Mat. Pura Appl.,1969