Few-shot　classification　aims　to　classify　samples　with　a　limited　quantity　of　labeled　training　data,　and　it　can　be　widely　applied　in　practical　scenarios　such　as　wastewater　treatment　plants　and　healthcare.　Compared　with　traditional　methods,　existing　deep　metric-based　algorithms　have　excelled　in　few-shot　classification　tasks,　but　some　issues　need　to　be　further　investigated.　While　current　standard　convolutional　networks　can　extract　expressive　depth　features,　they　do　not　fully　exploit　the　relationships　among　input　sample　attributes.　Two　problems　are　included　here:　(1)　how　to　extract　more　expressive　features　and　transform　them　into　attributes,　and　(2)　how　to　obtain　the　optimal　combination　of　sample　class　attributes.　This　paper　proposes　a　few-shot　classification　method　based　on　manifold　metric　learning　(MML)　with　feature　space　embedded　in　symmetric　positive　definite　(SPD)　manifolds　to　overcome　the　above　limitations.　First,　significant　features　are　extracted　using　the　proposed　joint　dynamic　convolution　module.　Second,　the　definition　and　properties　of　Riemannian　popular　strictly　convex　geodesics　are　used　to　minimize　the　proposed　MML　loss　function　and　obtain　the　optimal　attribute　correlation　matrix　A.　We　theoretically　prove　that　the　MML　is　popularly　strictly　convex　in　the　SPD　and　obtain　the　global　optimal　solution　in　the　closed　space.　Extensive　experimental　results　on　popular　datasets　show　that　our　proposed　approach　outperforms　other　state-of-the-art　methods.