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Rules and Examples 
General requirements for entry preparation:


FORMAT: In exceptional cases also Latex 2.09 is OK. The entry will be translated. Bibliography: without \bibitem command till 34 entries. Bibliography  if cited, then hard citations (without \cite command !!!). Please take into account all details below up to spaces. Equations: with \tag or \eqno command for numbering (only if needed) and \nonumber command. No \newcommand please!!! No \ref please!!! It is very much desirable that terms and articles have to be with corresponding _formulas_ on a strong mathematical level. The statements should be concise, but have to be made as inside body of an article, not as in introduction (several sentences without formulas with citations, as in Example 3 below). Please, add formulas to every word which implies them. For wellknown notions and terms it would be desirable to cite an article where it has appeared for the first time. Size of entries is not very much restricted: Entries can be written with coauthors (1 entry  till 2 authors, for review articles  till 3 authors). 
EXAMPLES  
Example 1. General structure of entry.  
%%%%%%%%%Begin of Entry%%%%%%%%%% \documentclass{article} % Your name BIBLIOGRAPHY. \end{document}


Example 2. Simple example of a term.  
%%%%%%%%%Begin of Entry%%%%%%%%%% \documentclass{article} % Ivanov BIBLIOGRAPHY. \end{document} %%%%%%%%%End of Entry%%%%%%%%%%%


Example 3. Undesirable and desirable styles of entry.  
Please save as text and latexing2e the below approximate example %%%%%%%%%Begin of example%%%%%%%%%% \documentclass{article} \begin{center} K\"{A}HLER MANIFOLD, a complex manifold which admits a K\"{a}hler metric [1] BIBLIOGRAPHY. \bigskip \begin{center} K\"{A}HLER MANIFOLD, a complex manifold $K$ having $U\left( N\right) $ holonomy admitting a Hermitian metric $g_{i\bar{j}}$ (called a \textit{K\"{a}hler metric} and can be written in complex coordinates $z_{i}$ through the K\"{a}hler potential $\varphi $ as $g_{i\bar{j}}=\frac{\partial ^{2}\varphi }{\partial z^{i}\partial \bar{z}^{j}}$) for which the fundamental form $\Omega =g_{i\bar{j}}dz_{i}\wedge d\bar{z}^{j}$ is closed $d\Omega =0$ [1]. Examples: any onedimensional complex manifold, complex $N$space, a projective manifold $CP_{N}$ and any its submanifold are K.M. The only nonvanishing Christoffel symbol of a K.M. is $\Gamma _{ij}^{k}=g^{k\bar{k}}\partial g_{i\bar{k}}/\partial z^{j}$ and the only nonvanishing component of the curvature tensor is $R_{ij\bar{k}}^{l}=\partial \Gamma _{ij}^{l}/\partial \bar{z}^{j}$. The theorem of CalabiYau: K.M. of vanishing first \textit{Chern class} $c_{1}\left( K\right) =0$ admits a \textit{K\"{a}hler metric} of $SU\left( N\right) $ holonomy. Such K.M. is Ricci flat $R_{ij}=0$ and admits nonvanishing covariantly constant spinor $% D_{i}\varepsilon =0$ which allows to exploit 6dimensional K.M. $K_{6}$ in superstring phenomenology [2] based on compactification scheme $M_{10}\rightarrow M_{4}\times K_{6}$, where $M_{4}$ is 4D maximally symmetric (de Sitter, antide Sitter or Minkowski) manifold [3]. BIBLIOGRAPHY. \end{document} %%%%%%%%%End of example%%%%%%%%%%%
