How does Byron's main character in "Manfred" represent a Byronic hero?
A Byronic hero is a tortured soul who is often reckless or violent, always brooding and introspective, and alienated from the rest of humanity. He isolates himself and suffers in solitude as a dark, misunderstood figure. Heathcliff in Wuthering Heights is a well-known example of the Byronic hero.
Manfred stands as well as as a fine example of the Byronic hero: he is tortured by the conviction that he destroyed Astarte, the woman he loved (though we are not given any details); he wanders alone in the Alps; he is on the brink of suicide when the Chamois Hunter saves him from that fate; he has to defend himself to the Chamois Hunter as not insane; and he questions and rebels against both the authority and "heaven or hell" doctrine of the Christian church. He is determined to face both life and death on his own terms and dies having refused to capitulate to institutionalized religion. He lives and dies as an individual who asserts his own will by refusing to conform to social norms.
There are many similarities between the protagonist in Byron's work and the Byronic Hero. The most dominant one is that Manfred, like the Byronic Hero, is someone cast apart from society. Simply put, he is "different." The Byronic Hero is one who is distinct from the social order. He is solitary and one in whom others stand in awe. Manfred is certainly this. The question upon which Manfred undertakes is one whose motivation is not entirely known. We understand that some internal demons animate and drive him, yet we do not fully understand what this exactly is, consistent with the Byronic Hero. Manfred is extremely adroit and skilled, another trait that is part of the archetype. Finally, when Manfred is able to accept his overall fate, the reader is able to see that Manfred is an overall decent human being, something that the Byronic Hero receives at the very end of the narrative.