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We study the ferromagnetic superconductor UCoGe at ambient pressure under ab-plane magnetic fields H, which are perpendicular to the ferromagnetic easy axis. It is shown that, by taking into account the Dyaloshinskii-Moriya interaction arising from the zigzag chain crystal structure of UCoGe, we can qualitatively explain the experimentally observed in-plane anisotropy for critical magnetic fields of the paramagnetic transition. Because of this strong dependence on the magnetic field direction, upper critical fields of superconductivity, which is mediated by ferromagnetic spin fluctuations, also become strongly anisotropic. The experimental observation of S-shaped Hc2‖b axis is qualitatively explained as a result of enhancement of the spin fluctuations due to decreased Curie temperature by the b-axis magnetic field. We also show that the S-shaped Hc2 is accompanied by a rotation of the d vector, which would be a key to understand the experiments not only at ambient pressure but also under pressure. [ABSTRACT FROM AUTHOR]