The Hobbesian Concept of Fear
According to Hobbes, fear is the ultimate motif. Fear, according to Hobbes, suffuses and shapes human life.
Now, I will present to you some quotes:
The hobbesian man is drive by pride but above all, by fear of other men.
He lives in constant fear of his life because he is bloated with unnatural passions such as pride, which cause men to invade one another.
Hopefully, we can now simply agree on Hobbes' concept of fear. Now let's link it to love.
The Hobbesian Concept of Love
I will present to you several quotes from Thomas Hobbes himself (can be found in his Leviathan):
What quality soever maketh a man beloved or feared of many, or the reputation of such quality, is power; because it is a means to have the assistance and service of many.
To Hobbes, it does not matter if one is feared or loved, as long as he attains power.
To show any sign of love or fear of another is honour; for both to love and to fear is to value. To contemn, or less to love or fear than he expects, is to dishonour; for it is undervaluing.
Again, Hobbes does not make a distinction between love and fear, just that in either case they attain values for a person.
And therefore to be honoured, loved, or feared of many is honourable, as arguments of power. To be honoured of few or none, dishonourable.
Therefore, Hobbes doesn't really care. He doesn't make a distinction between the two. According to him, all that matters is attaining honour and if that means attracting the love or even fear of others, then so be it.
This, therefore, is how love is related to fear. As a means of attaining honour, power and values. However, based on my own interpretation, I don't believe that Hobbes believes that the love expressed by the people is genuine, rather merely a means of expressing their agreement.
EDIT: The above quotations are from Part I, Chapter X of Hobbes's Leviathan, which can be found here.