same.py

def same(i):
    a = next(i)
    return _same(a, i)

def _same(a, i):
    try:
        b = next(i)
    except StopIteration:
        return True

    if a != b:
        return False
    return _same(a, i)

assert same(iter([1,2,3])) is False
assert same(iter([1])) 
assert same(iter([1,1,1]))

In Python, it's important to remember you also have unsized interables so your solution is nice but recursion will fail if you got more than 1000 items on a standard CPython config. Plus that equality is not the same as idententy, and both should be something you want to check against. So:

def same(it, cmp=operator.eq):
    g = iter(it)
    s = next(g, None)
    return all(cmp(s, x) for x in g)