[latexpage]
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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*}