Extractive speech summarization is intended to produce a condensed version of the original spoken document by selecting a few salient sentences from the document and concatenate them together to form a summary. In this paper, we study a novel use of manifold learning techniques for extractive speech summarization. Manifold learning has experienced a surge of research interest in various domains concerned with dimensionality reduction and data representation recently, but has so far been largely under-explored in extractive text or speech summarization. Our contributions in this paper are at least twofold. First, we explore the use of several manifold learning algorithms to capture the latent semantic information of sentences for enhanced extractive speech summarization, including isometric feature mapping (ISOMAP), locally linear embedding (LLE) and Laplacian eigenmap. Second, the merits of our proposed summarization methods and several widely-used methods are extensively analyzed and compared. The empirical results demonstrate the effectiveness of our unsupervised summarization methods, in relation to several state-of-the-art methods. In particular, a synergy of the manifold learning based methods and state-of-the-art methods, such as the integer linear programming (ILP) method, contributes to further gains in summarization performance.