We discuss the spin-wave dispersion in a triple- \(\textbf{Q}\) noncoplanar state with nonzero net chirality realized in the \(J_1\) - \(J_3\) classical Heisenberg model on the breathing-kagome lattice. By performing the spin-wave expansion, we show that the spin wave experiences a spatially inhomogeneous geometric phase in propagating on a curved space spanned by the noncoplanar spins and resultantly, its dispersion becomes asymmetric with respect to the \(\Gamma \) point, suggestive of a nonreciprocal spin transport. From the real-space perspective, we argue that a scalar spin chirality defined in a straight line is associated with the geometric-phase effect.
