The lower bound on the period of uniform rotation of neutron stars ( NS ) with causal equation of state ( EOS ) , P _ { min } , is shown to be determined , with a high precision , by the upper bound on the surface redshift of static neutron star models , z _ { max } .
We obtain z _ { max } = 0.851 , which turns out to be about 5 \% lower than upper bound obtained by Lindblom ( 1984 ) .
Using then the empirical formula for the maximum rotation frequency of uniform rotation of neutron star models with realistic causal EOS , derived by Lasota et al .
( 1996 ) , we establish an approximate relation between z _ { max } and P _ { min } , in which P _ { min } is proportional to the maximum mass of static NS , M _ { s } ^ { max } .
In this way we reproduce , within 2 % , the exact formula of Koranda et al .
( 1997 ) based on extensive exact numerical calculations .
Replacing M _ { s } ^ { max } by the maximum measured NS mass , 1.442 ~ { } M _ { \odot } , we get a lower bound P _ { min } \simeq 0.288 ms .