"codifferential" meaning in English

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  "etymology_text": "co- + differential",
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          "ref": "2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv",
          "text": "In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #x5C;begin#x7B;matrix#x7D;#x5C;partial#x5F;t#x5C;omega#x2B;#x7B;#x5C;mathcalL#x7D;#x5F;u#x5C;omega#x26;#x3D;0#x5C;#x5C;u#x26;#x3D;#x5C;delta#x5C;tilde#x5C;eta#x7B;-1#x7D;#x5C;Delta#x7B;-1#x7D;#x5C;omega#x5C;end#x7B;matrix#x7D; where #x5C;omega is the vorticity 2-form, #x7B;#x5C;mathcalL#x7D;#x5F;u denotes the Lie derivative with respect to the velocity field u, #x5C;Delta is the Hodge Laplacian, #x5C;delta is the codifferential (the negative of the divergence operator), and #x5C;tilde#x5C;eta#x7B;-1#x7D; is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric #x5C;eta.",
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      "glosses": [
        "The projected differential of an extensor field."
      ],
      "id": "en-codifferential-en-noun-s9GGSNJj",
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        "(mathematics) The projected differential of an extensor field."
      ],
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          "ref": "2015, 1:19:34 from the start, in 2 Tangent Space, Differential Forms, Metric (Mathematics for Theoretical Physicists - Hirosi Ooguri), spoken by Hiroshi Ooguri (Hiroshi Ooguri), K Raviteja (YouTube)",
          "text": "One important concept is the introduction of codifferential operator",
          "type": "quotation"
        }
      ],
      "glosses": [
        "the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
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          "differential geometry",
          "differential geometry"
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          "exterior derivative",
          "exterior derivative"
        ],
        [
          "divergence",
          "divergence"
        ],
        [
          "Hodge star",
          "Hodge star"
        ],
        [
          "Hermitian conjugate",
          "Hermitian conjugate"
        ],
        [
          "inner product",
          "inner product"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
      ]
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  "word": "codifferential"
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  "etymology_text": "co- + differential",
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        "The projected differential of an extensor field."
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        "(mathematics) The projected differential of an extensor field."
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          "ref": "2015, 1:19:34 from the start, in 2 Tangent Space, Differential Forms, Metric (Mathematics for Theoretical Physicists - Hirosi Ooguri), spoken by Hiroshi Ooguri (Hiroshi Ooguri), K Raviteja (YouTube)",
          "text": "One important concept is the introduction of codifferential operator",
          "type": "quotation"
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      ],
      "glosses": [
        "the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
      ],
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          "exterior derivative",
          "exterior derivative"
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          "divergence",
          "divergence"
        ],
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          "Hodge star",
          "Hodge star"
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        "(differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
      ]
    }
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  "word": "codifferential"
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