Artur Palha

Notation

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Differential k-form:

Greek letters with superscript in parenthesis indicating the type of form (k-form):

    \begin{equation*} \alpha^{(k)},\,\,\,\beta^{(1)},\,\,\,\gamma^{(3)},\,\,\,\omega^{(2)}\,. \end{equation*}

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Differential k-form (components):

Greek letters with superscript in parenthesis indicating the type of form (k-form) and a subscript indicating the component:

    \begin{equation*} \alpha^{(k)}_{i},\,\,\,\beta^{(1)}_{2},\,\,\,\gamma^{(3)}_{l},\,\,\,\omega^{(2)}_{2}\,. \end{equation*}

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Scalar field:

Latin letters and in some cases greek letters:

    \begin{equation*} a, \,\,\, f,\,\,\, g,\,\,\, \phi,\,\,\,\varphi\,. \end{equation*}

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Tensor operator:

Bold capital serif latin characters:

    \begin{equation*} \boldsymbol{\mathsf{A}},\,\,\, \boldsymbol{\mathsf{B}},\,\,\,\boldsymbol{\mathsf{S}}\,. \end{equation*}

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Tensor operator (coefficients):

Capital serif latin characters with subscript indices:

    \begin{equation*} \mathsf{A}_{ij},\,\,\, \mathsf{B}_{ikmn},\,\,\,\mathsf{S}_{lk}\,. \end{equation*}

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Vector:

Bold serif latin characters:

    \begin{equation*} \boldsymbol{\mathsf{a}},\,\,\, \boldsymbol{\mathsf{b}},\,\,\,\boldsymbol{\mathsf{c}},\,\,\, \boldsymbol{\mathsf{v}}\,. \end{equation*}

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Vector (coefficients):

Serif latin characters with a subscript index:

    \begin{equation*} \mathsf{a}_{i},\,\,\, \mathsf{b}_{j},\,\,\,\mathsf{c}_{k},\,\,\, \mathsf{v}_{n}\,. \end{equation*}

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Vector field:

Latin characters:

    \begin{equation*} \vec{a},\,\,\, \vec{b},\,\,\,\vec{c},\,\,\, \vec{v}\,. \end{equation*}

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Vector field (components):

Latin characters with either a subscript index (vector calculus notation) or superscript (differential geometry notation):

    \begin{equation*} a_{i},\,\,\, b_{k},\,\,\,c_{l},\,\,\, v_{j}\qquad \text{(vector calculus notation)}, \end{equation*}

    \begin{equation*} a^{i},\,\,\, b^{k},\,\,\,c^{l},\,\,\, v^{j}\qquad \text{(differential geometry notation)}. \end{equation*}