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A relation among the effective nucleon mass $M^*$, the incompressibility $K$and the effective $\sigma$-meson mass $m_{\rm s}^*$ in nuclear matter isstudied by using the relativistic nuclear model. We found that there is astrong correlation between $M^*$ and $m_{\rm s}^*$, while there is only a weakcorrelation between $K$ and $m_{\rm s}^*$. At the normal density, $m_{\rm s}^*$is smaller than the one at zero density, if $M^*$ is smaller than 0.8 times ofthe nucleon mass at zero density. It is also found that the off-shell effectivemass $\mu_{\rm s}^*$ is related directly to $K$ and $M^*$ at the normaldensity.Comment: 10 pages, containing 7 eps figure

A RELATION AMONG THE EFFECTIVE NUCLEON MASS, THE INCOMPRESSIBILITY AND THE EFFECTIVE σ-MESON MASS IN NUCLEAR MATTER