The conventional Singleton (anti-)pattern isn't a collection of static variables; rather, it is an object with non-static members, of which only one instance can exist.
In C++, this allows you to avoid the biggest problem with static variables: the "initialisation order fiasco". Because the initialisation order is unspecified for static variables in different translation units, there's a danger that the constructor of one might try to access another before it is initialised, giving undefined behaviour. However, it introduces other problems (a similar "destruction order fiasco", and thread safety issues in older compilers), so it's still something to avoid.
If you want a collection of static variables and functions, then put them in a namespace rather than a class:
namespace stuff {
int a;
void do_something();
}
If you think you want a singleton, then think again; you're generally better avoiding globally accessible objects altogether. If you still want one, then you would make a class with a private constructor, and a public accessor that returns a reference to the single instance, along the lines of:
class singleton {
public:
singleton & get() {
static singleton instance;
return instance;
}
int a;
void do_something();
private:
singleton() {}
~singleton() {}
singleton(singleton const &) = delete;
};