# 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*}