\documentclass[draft, jgsp]{geom}

\begin{document}
\head{75}{2026}
\thispagestyle{plain}

\title{Here Comes the Title}
\author{Here Come(s) the Author(s) Name(s)}
\date{}
\maketitle



\smallskip
\begin{abstract}
Here comes the abstract of less then $100$ words. Formulas and citations
should be avoided!\\[0.2cm]
\textsl{MSC}: in ascending order \\
\textsl{Keywords}: In alphabetical order separated by commas.
The first keyword starts with a capital letter, the rest with a lowercase letter.
\end{abstract}

\label{first}
\section{Introduction\label{sec:intro}}

This document is a printout of the file \verb"jgsp-sample.tex" and
it describes in some detail the use of the JGSP class file
\verb"geom.cls" for the preparation of articles to be submitted
for publication in Journal of Geometry and Symmetry in Physics.

In general the potential authors should use the standard \LaTeX{}
commands as much as possible. Personal macros should be used
only when it is absolutely necessary and have to be put always
in the preamble.
It is mandatory to remove all comments from your \verb"tex" file before submission.


\section{Some Section, e.g.\ How to Start\label{sec:start}}

The titles of the Sections and that ones of Subsections should be
typed following the style of capitalization exemplified above and
below (i.e., using Initial Capitals).

\begin{definition}\label{def:1}
Definitions, propositions, lemmas, theorems, equations, etc.\ should be
introduced using the appropriate environment and labelled.
Please make use of the respective labels when you refer to any of them.
\end{definition}

\begin{corollary}\label{cor1}
This results in fewer errors in processing and saves authors and
editors proofreading times.
\end{corollary}

\subsection{Some Subsection -- How to Enter Mathematics\label{ssec:math}}

Use $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{Z}$ to denote
the real, complex, quaternion and integer numbers, respectively,
and $\mathbb{R}^n$, $\mathbb{C}^n$, $\mathbb{H}^n$, $\mathbb{Z}^n$
for spaces built on them. The spheres, projective, Euclidean, Lorentz,
etc.\ spaces should be denoted in analogous way. The Lie groups should
be typeset by upright capital letters the only exceptions being
the symplectic and spinorial groups which should be typed as
$\mathrm{Sp}(2n,\mathbb{R})$, $\mathrm{Sp}(2n,\mathbb{C})$ and
$\mathrm{Spin}(n)$. The respective Lie algebras should be typed by small
Gothic letters, i.e., $\mathfrak{g}$, $\mathfrak{gl}$, $\mathfrak{sl}$,
$\mathfrak{so}$, $\mathfrak{su}$, $\mathfrak{sp}$, $\mathfrak{spin}$,
etc.\ with an indication about their dimension and the field over which
they are considered (when this is not unambiguously clear by the context),
e.g., $\mathfrak{gl}(n,\mathbb{C})$, $\mathfrak{sl}(n,\mathbb{R})$,
$\mathfrak{so}(n,\mathbb{C})$, $\mathfrak{su}(n)$,
$\mathfrak{sp}(2n,\mathbb{R})$, $\mathfrak{spin}(n)$ and so on.

The real and imaginary parts of a number, matrix, respectively,
the image and the kernel of a map, operator, and the identity
operator should be introduced by the commands
\begin{verbatim}
\Re, \Im, \im, \ker and \Id
\end{verbatim}
which will produce respectively  $\Re$, $\Im$, $\im$, $\ker$ and $\Id$.

Some formulas
\begin{gather}
I=E\,\rd u^2+2F\,\rd u\,\rd v+G\,\rd v^2,
\qquad
II=L\,\rd u^2+2M\,\rd u\,\rd v+N\,\rd v^2\\
\theta(\mathbf{z})=\sum_{\mathbf{n}\in\mathcal{Z}^g}
\exp\left(\ri\pi\langle\mathbf{n},B\mathbf{n}\rangle +
2\langle\mathbf{n},\mathbf{z}\rangle\right),
\qquad
\mathbf{z}\in\mathbb{C}^g.
\end{gather}
Spaces: Everywhere where  it is  POSSIBLE  please, use the \verb"\qquad" command in displayed formulas,
if this is  not possible  --  use  \verb"\quad".
\begin{example}
Consider the Euler equations
\begin{align}
\dot{x}_1&=\frac{I_2-I_3}{I_2I_3}x_2x_3\notag\\
\dot{x}_2&=\frac{I_3-I_1}{I_3I_1}x_3x_1\label{e}\\
\dot{x}_3&=\frac{I_1-I_2}{I_1I_2}x_1x_2.\notag
\end{align}
\end{example}
Please, DO NOT SEPARATE  the equations which appear on different lines
by COMMAS as exemplified above, but put a full stop at the very end.\\
Sets, spaces, etc.\ should be introduced in the following format:
\begin{align*}
\mathbb{S}^n & = \{x\in\mathbb{R}^{n+1} \semicolon \|x\|=1\}\\
\mathfrak{sl}(n,\mathbb{R}) & = \{X\in\Mat(n,\mathbb{R}) \semicolon \tr(X)=0\}\\
\U(m,n-m) & = \{g\in\GL(n,\mathbb{C}) \semicolon
g\epsilon g^{\dagger}=\epsilon,\; \det g=1\}.
\end{align*}
Notice   especially the use of  SEMICOLON (\verb"\semicolon")  command inside!


\subsubsection{Some Subsubsection\label{ssec:ss}}

\begin{theorem}\label{somelabel}
Some Theorem.
\end{theorem}

\section{Another Section -- How to Include Graphics\label{sec:gr}}

This should be done following the example given below. Let us mention
however that the submitted graphics are expected to be in one of
the following graphic formats: jpg, png, pdf or eps (Encapsulated Post
Script). If they are prepared via some graphics package, scanning
photographs or other computer way for generating images the authors
should avoid the use of any lines thinner than $0.5$ points of width.
The resolution of the figures and other illustrations should be not
less than $300$~dpi.
%Note that this example needs the line
%\begin{verbatim}
%\usepackage[...]{graphicx}
%\end{verbatim}
%in the preamble of your document and
%
%You have to delete
%\verb"\begin{verbatim}" and \verb"\end{verbatim}"
%from the figure environment in order that the graphicx
%package becomes operational.

\begin{small}
\begin{verbatim}
\begin{figure}
\centerline{\includegraphics[width=XXX]{file_name.eps}}
\caption{This is the caption of the figure.}
\end{figure}
\end{verbatim}
\end{small}

\section{Yet Another Section -- Personal information\label{sec:yas}}

The article ends with some personal information for every author.
For this purpose it is necessary personal photos with dimensions
$30\times 40$~mm (not less $300$~dpi) to be provided.
These photos will be printed in color.
That is why they have to be in \verb"cmik" color model.
Else they will be comverted from \verb"rgb" to \verb"cmyk".

\begin{remark}
For example see the end of these guidelines.
\end{remark}

%\begin{lemma}\label{lemma_l2}
%Another Lemma.
%\end{lemma}

\section*{Acknowledgements}

Write here your acknowledgements to respective persons (without their  Titles!) or Institutions.

\section*{Bibliography}

References should be indicated in the text by square-bracketed
numbers (produced by the respective labels in the \LaTeX{} file)
and listed in \textbf{alphabetical} order (by first author) with
\textbf{full details} following \textbf{exactly} the samples
given below in the bibliography section for journal articles,
books and a paper in a proceedings volume. Please, note especially
the \textbf{capitalization} of titles and the \textbf{absence} of
the initials of the middle names!!

\appendix

\section{File \texttt{somedef.tex}}

The following table shows the special  commands defined in \verb"geomdef.tex".

\begin{table}[h]
\centering
\begin{tabular}[t]{|l|l|l|}
\hline
Command&Print&Type\\
\hline
\verb"\semicolon"&$\semicolon$&\\
\verb"\rd"&$\rd$&\\
\verb"\re"&$\re$&\\
\verb"\ri"&$\ri$&\\
\verb"\diag"&$\diag$&Operator\\
\verb"\Div"&$\Div$&Operator\\
\verb"\Exp"&$\Exp$&Operator\\
\verb"\gyr"&$\gyr$&Operator\\
\verb"\id"&$\id$&Operator\\
\verb"\Id"&$\Id$&Operator\\
\verb"\Lie"&$\Lie$&Operator\\
\verb"\sign"&$\sign$&Operator\\
\verb"\Sgn"&$\Sgn$&Operator\\
\verb"\Span"&$\Span$&Operator\\
\verb"\Stab"&$\Stab$&Operator\\
\verb"\Sym"&$\Sym$&Operator\\
\verb"\tr"&$\tr$&Operator\\
\verb"\Tr"&$\Tr$&Operator\\
\verb"\trace"&$\trace$&Operator\\
\verb"\Trace"&$\Trace$&Operator\\
\hline
\end{tabular}
\qquad
\begin{tabular}[t]{|l|l|l|}
\hline
Command&Print&Type\\
\hline
\verb"\Ad"&$\Ad$&Upright text\\
\verb"\ad"&$\ad$&Upright text\\
\verb"\AdS"&$\AdS$&Upright text\\
\verb"\Aff"&$\Aff$&Upright text\\
\verb"\im"&$\im$&Upright text\\
\verb"\Sp"&$\Sp$&Upright text\\
\verb"\Gr"&$\Gr$&Upright text\\
\verb"\GL"&$\GL$&Upright text\\
\verb"\PGL"&$\PGL$&Upright text\\
\verb"\SL"&$\SL$&Upright text\\
\verb"\PSL"&$\PSL$&Upright text\\
\verb"\SO"&$\SO$&Upright text\\
\verb"\SU"&$\SU$&Upright text\\
\verb"\U"&$\U$&Upright text\\
\verb"\col"&$\col$&Upright text\\
\verb"\Mat"&$\Mat$&Upright text\\
\verb"\const"&$\const$&Upright text\\
\verb"\nD"&$\nD$&\\
\hline
\end{tabular}
\end{table}

The predifined theorem-like environments are:
\verb"definition",
\verb"theorem",
\verb"lemma",
\verb"proposition",
\verb"corollary",
\verb"example",
\verb"conjecture",
\verb"remark",
\verb"remarks".\\[2mm]

 {\Large NB When submitting  the  manuscript - please, eliminate  ALL personal comments  from
the LaTeX file!}

\begin{thebibliography}{9}\itemsep=-.2pc

\bibitem{hel}
Helgason S.,
\emph{Differential Geometry, Lie Groups and Symmetric Spaces},
Academic Press, Toronto 1978.

\bibitem{ken}
Kenmotsu K.,
\emph{Surfaces of Revolution with Prescribed Mean Curvature},
T\^ohoku Math. J. \textbf{32} (1980) 147--153.

\bibitem{nab}
Naber G.,
\emph{Topology, Geometry and Physics: Background for the Witten Conjecture II},
J. Geom. Symmetry Phys.  \textbf{3} (2004) 27--123.

\bibitem{opr2}
Oprea J.,
\emph{Differential Geometry and Its Applications}, 2$^{\rm nd}$ Edn,
Prentice Hall, New Jersey 2003.

\bibitem{pau}
Paulsen W.,
\emph{What is the Shape of the Mylar Balloon?},
Amer. Math. Monthly \textbf{101} (1994) 953--958.

\bibitem{pul}
Pulov V., Hadzhilazova M. and Mladenov I.,
\emph{On a Class of Linear Weingarten Surfaces},
Geom. Integr.  Quantization \textbf{19} (2018) 168--187.

\bibitem{z-g-k}
Zlatanov S. and Petrov A.,
\emph{Thin Shells Deforming Without Bending Under Standard Loads} (in Russian),
In: Reliability of New Types of Transport Vessels, Leningrad 1983, pp 25--34.
\end{thebibliography}


\bigskip
\intextsep 0pt
\begin{wrapfigure}{l}{30mm}
\includegraphics{Blur}
\end{wrapfigure}
Dr.~\dots, a Senior Engineer, received his PhD from the Institute of
Mathematics at \dots\dots University in \dots. His research interests
span \dots\dots

More information. More information. More information.
His major contributions include the theory and applications of \dots
Representative achievements include \dots
He had published the professional book \dots in \dots.
Dr \dots\ can be contacted at \emph{E-mail address}: {\tt xyz@gmail.com}.\\

\bigskip
Address\\
Department of  Mathematics and Informatics,
Kliment Ohridski University of Sofia\\
Sofia 1164, BULGARIA\\

Same for other author(s).

\label{last}
\end{document}
