\documentclass[11pt,twoside]{gsp}

\def\semicolon{\nobreak\mskip2mu\mathpunct{}\nonscript\mkern-\thinmuskip{;}
\mskip6muplus1mu\relax} % This defines the semicolon command

\input somedef

\setcounter{page}{1}

\begin{document}

\thispagestyle{plain}

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

\date{}


\maketitle


\comm{Communicated by XXX}\

\begin{abstract}
Here comes the abstract of less than $100$ words. Formulas and
citations should be avoided.\\[0.2cm]
 \textsl{MSC}:\\
 \textsl{Keywords}:
\end{abstract}


\label{first}

\section[]{Introduction}
This document is a printout of the file jgsp-sample.tex and it
describes in some detail the use of the JGSP class file gsp.cls
for the preparation of articles to be submitted for publication in
the 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.





\section{Some Section, e.g. How to 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}


Please type differential$(\d)$, exponent$(\e )$ and imaginary unit
$(\i)$ using \verb|$\d$|, \verb|$\e$|, \verb|$\i$|. 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 exeptions
being the symplectic and spinorial groups which should be typed as
${\rm Sp}(2n,{\mathbb R})$, ${\rm Sp}(2n,{\mathbb C})$ and ${\rm
Spin}(n)$. The respective Lie algebras should be typed by small
gothic letters, i.e., $\frak{g, gl,  sl, so, su, sp, spin},$ 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., $\frak{gl}(n,{\mathbb C})$  $\frak{sl}(n,{\mathbb
R})$, $\frak{so}(n,{\mathbb C})$, $\frak{su}(n)$,
$\frak{sp}(2n,{\mathbb R})$,
$\frak{spin}(n)$ 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  $\Re, \Im, \im$, $\ker$ and $\Id$.


Some formulas:
\begin{equation}
I=E\,\d u^2+2F\,\d u\,\d v+G\,\d v^2
\end{equation}

\begin{equation}
\theta(\mathbf{z})=\sum_{\mathbf{n}\in{\mathcal Z}^g} \exp
\left(\i\pi\langle\mathbf{n},B\mathbf{n}\rangle+
2\langle\mathbf{n}, \mathbf{z}\rangle\right), \quad
\mathbf{z}\in\mathbb{C}^g.
\end{equation}

\begin{example}
Consider the Euler equations
\begin{align}
\dot{x}_1&=\displaystyle{\frac{I_2-I_3}{I_2I_3}}x_2x_3\notag\\
\dot{x}_2&=\displaystyle{\frac{I_3-I_1}{I_3I_1}}x_3x_1\label{e}\\
\dot{x}_3&=\displaystyle{\frac{I_1-I_2}{I_1I_2}}x_1x_2.\notag
\end{align}
\end{example}
Please, do not separate 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:
$$
\begin{array}{rcl}
{\mathbb S}^n &=& \{x \in {\mathbb R}^{n + 1}  \semicolon
||x|| = 1 \}\\
\frak{sl}(n,{\mathbb R}) &=&\{X \in {\rm Mat}(n,{\mathbb R})  \semicolon
{\rm tr}(X)= 0 \}\\
{\rm U}(m,n-m) &= & \{g \in {\rm GL}(n,{\mathbb C})  \semicolon
g\epsilon g^{\dagger} = \epsilon \}.
\end{array}$$

Please, note the use of semicolon command inside.


\subsubsection{Some Subsubsection}


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

\section{Another Section - How to Include  Graphics}

This should be done following the example given below. Let us
mention however that the submitted graphics are expected to be
Encapsulated Post Scripts  files (name.eps). 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. Note that this example
needs the line
\begin{verbatim}
\usepackage[...]{graphicx}
\end{verbatim}
in the preamble of your document and  you have to delete
\begin{verbatim}
\begin- and \end-{verbatim}
\end{verbatim} from the figure environment in order that the graphicx
package becomes operational. The resolution of the figures and
other illustrations should be not less  than $300$dpi.


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



\section{Yet Another Section}

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


\section*{Acknowledgements}
Write here your acknowledgements to respective persons 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 ALPHABETICAL order (by first author) with
FULL DETAILS following EXACTLY  the samples given below in the
bibliography section for journal articles, books and a paper in a
proceedings volume. Please, note  especially the CAPITALIZATION
of titles and the ABSENCE of the initials of the middle names!!



\begin{thebibliography}{99}\itemsep=-.2pc

\bibitem{fed} Feder T., {\it Strong Near Subgroups and Left Gyrogroups,} J. Algebra
{\bf259} (2003) 177--190.

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

\bibitem{ken} Kenmotsu K., {\it Surfaces of Revolution with Prescribed Mean Curvature},
T{\^ o}hoku Math. J. {\bf 32} (1980) 147-153.

\bibitem{k-t} Konopelchenko B. and Taimanov I., {\it  Constant Mean Curvature Surfaces via
an Integrable Dynamical System}, J. Phys. A: Math. Gen. {\bf 29}
(1996) 1261-1265.

\bibitem{opr1} Oprea J., {\it The Mathematics of Soap Films:
Explorations with Maple}$^{^{\circledR}}$, AMS, Providence 2000.

\bibitem{opr2} Oprea J., {\it Differential Geometry and Its Applications}, Second Edition,
 Prentice Hall, New Jersey 2003.

\bibitem{oss} Osserman R, {\it A Survey of Minimal Surfaces},
Dover, New York 1986.


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

 \bibitem{wil} Willmore T., {\it An Introduction to Differential Geometry},
 Second Edition, Oxford Univ. Press, Oxford 1982.

 \bibitem{z-g-k} Zlatanov S., Grahovski G. and Kostov A.,
 {\it Second Order Reductions of $N$-wave Interactions Related to Low--rank
 Simple Lie Algebras},  In: Geometry, Integrability and Quantization,
I. Mladenov and G. Naber (Eds),   Coral Press,  Sofia 2000, pp
55--77.

\end{thebibliography}


Insert here your data,  e.g.\\
 Azniv Kasparian \\
Dept.  Math \& Informatics \\
Kliment Ohridski University of Sofia\\
Sofia 1164, Bulgaria\\
{\it E-mail address}: {\tt kasparia@fmi.uni-sofia.bg}\\[0.3cm]
Abraham  A. Ungar \\
 Department of Mathematics \\
 North Dakota State University\\
 Fargo, North Dakota 58105\\
USA \\
{\it E-mail address}: {\tt Abraham.Ungar@ndsu.edu}


\label{last}
\end{document}

$\frak{so}(4), \frak{sl}(2,{\mathbb R})$

.
