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In this paper, we investigate the relation between the curvature of thephysical space and the deformation function of the deformed oscillator algebrausing non-linear coherent states approach. For this purpose, we studytwo-dimensional harmonic oscillators on the flat surface and on a sphere byapplying the Higgs modell. With the use of their algebras, we show that thetwo-dimensional oscillator algebra on a surface can be considered as a deformedone-dimensional oscillator algebra where the effect of the curvature of thesurface is appeared as a deformation function. We also show that the curvatureof the physical space plays the role of deformation parameter. Then weconstruct the associated coherent states on the flat surface and on a sphereand compare their quantum statistical properties, including quadraturesqueezing and antibunching effect.Comment: 12 pages, 7 figs. To be appeared in J. Phys.

Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator