Single-crystalline perovskite oxide membranes provide a powerful platform to access physical properties that are inaccessible in bulk crystals and substrate-clamped thin films. Within this context, the deliberate fabrication of tailored corrugations provides a reliable mean to impose local curvature enabling deterministic modulation of functional properties. Here, we demonstrate controlled topographic patterning in (00l)-oriented La_(0.7)Sr_(0.3)MnO₃ (LSMO) membranes with thicknesses ranging from 4 to 100 nm where they spontaneously form sinusoidal wrinkles with thickness-dependent periodicity and amplitude. The wrinkle morphology directly modulates membrane stiffness and generates exceptionally large local strains exceeding 5% with strain gradients approaching ∼ 2.5 x 10⁷ m⁻¹ in the thinnest membranes. These extreme deformations suppress antiferrodistortive octahedral rotations and stabilize polar distortions, evidencing a curvature-driven symmetry transformation. The surface potential variation reinforces the formation of wrinkled-induced polar patterns being strongly modulated with thickness. The variation of Mn oxidation state from ∼ 3.2+ to ∼ 2.85+ provides a direct chemical signature of a thickness-controlled electronic transition. These results demonstrate that corrugation-induced strain gradients in oxide membranes with different thicknesses can drive coupled structural, nanomechanical and electronic transformations, offering a singular route to engineer their functional states for next-generation electronic devices.