Machine unlearning is a fundamental mechanism that enforces the right to be forgotten. Existing unlearning studies that rely on label manipulation or task-gradient reversal often deliver limited unlearning effectiveness. Moreover, they can undermine the original learning objective and typically do not guarantee equivalence to standard unlearning by retraining. In this paper, we propose \textbf{ManiF-SMC} (\textbf{Mani}fold \textbf{F}orgetting with \textbf{S}elf \textbf{M}ode \textbf{C}onnectivity), motivated by the observation that a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data. We begin with systematically recasting the approximate unlearning as pushing each erased sample away from its original learned manifold representation centroid toward its nearest semantic neighbors in the retained data. This reformulation aligns unlearning with retraining behavior and operates purely in representation space, reducing reliance on labels and task-specific gradients. To tackle the manifold representation-based unlearning problem, ManiF-SMC encapsulates the unlearning and representation preservation goals in a margin-based triplet loss. Because finding a suitable margin for unlearning is challenging, we propose a self-mode-connectivity module that rapidly reconstructs the local manifold to guide the adaptive margins generation for each unlearning case. Extensive experiments on four representative datasets show that ManiF-SMC achieves unlearning effectiveness comparable to state-of-the-art approximate methods while operating solely within the model's representation space.