jQuery: Target ONLY Safari

(Edit so that Chrome must not be in the user agent):

(Edit2 because Chrome for iOS has "CriOS" instead of "Chrome" in its user agent):

if (
    navigator.userAgent.indexOf('Safari') != -1 && 
    navigator.userAgent.indexOf('Chrome') == -1 && 
    navigator.userAgent.indexOf('CriOS/') == -1
)  { 
   //i.e. apply safari class via jquery
}

P.S. You should consider using Feature Detection to change your website according to what the current browser can do instead of checking for user agents, which you have to update regulary.

if (navigator.userAgent.indexOf('Safari') && !navigator.userAgent.indexOf('Chrome')) {
    // Yep, it's Safari =)
}else {
    // Nope, it's another browser =(
}