"smooth manifold" meaning in English

{
  "forms": [
    {
      "form": "smooth manifolds",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth manifold (plural smooth manifolds)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Manifolds",
          "orig": "en:Manifolds",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "A manifold which is infinitely differentiable (C ᪲)."
      ],
      "hypernyms": [
        {
          "word": "topological manifold"
        }
      ],
      "hyponyms": [
        {
          "word": "Riemannian manifold"
        }
      ],
      "id": "en-smooth_manifold-en-noun-DhBiWSWu",
      "links": [
        [
          "manifold",
          "manifold"
        ],
        [
          "infinitely",
          "infinitely"
        ],
        [
          "differentiable",
          "differentiable"
        ]
      ],
      "synonyms": [
        {
          "word": "differentiable manifold"
        }
      ]
    }
  ],
  "word": "smooth manifold"
}

{
  "forms": [
    {
      "form": "smooth manifolds",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth manifold (plural smooth manifolds)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "topological manifold"
    }
  ],
  "hyponyms": [
    {
      "word": "Riemannian manifold"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Manifolds"
      ],
      "glosses": [
        "A manifold which is infinitely differentiable (C ᪲)."
      ],
      "links": [
        [
          "manifold",
          "manifold"
        ],
        [
          "infinitely",
          "infinitely"
        ],
        [
          "differentiable",
          "differentiable"
        ]
      ]
    }
  ],
  "synonyms": [
    {
      "word": "differentiable manifold"
    }
  ],
  "word": "smooth manifold"
}