Note that the references are sorted alphabetically.
I will use SnO as an abbreviation of Sora No Otoshimono (Heaven's Lost Property's Japanese title).
In Sora No Otoshimono, Aegis is a defense system used by Angeloids to protect themselves.
In Greek Mythology, Aegis is a shield made out of animal skin carried by Zeus and Athena.
Alpha, Beta, ...
The Angeloids code name are all greeks letters
Oregano is the only angeloid character not code named. This is explained by the fact that she was not designed to be an unique model, but just another medical robot who went out to the human world by accident.
Note that if we follow the order of apparition of the Angeloids, their code names are alphabetically sorted.
Ikaros' bow is named Apollon.
It is an obvious reference to the God Apollo. Even though Apollo is known for being the God of Music and Poetry, he also has a golden bow. The bow can cause health or famine, although its main function is that of a regular bow, but with much greater power.
In a similar way, Ikaros' bow is known for having great power, as she could destroy cities and countries with a few arrows.
Ikaros has the ability to shoot missiles using Artemis.
Artemis is Apollo's twin sister. She is known as the hunt, wild animals, wilderness, childbirth, virginity and protector of young girls.
She carries a silver bow made to kill without pain, opposed to Apollo's golden bow (see Apollo's reference) which is made to bring great suffering.
The weapon and the divinity are linked on a particular point : Ikaros' Artemis missiles are designed to follow its target until it reaches it. We can link this to Artemis' bow which is made for hunt, therefore for tracking.
Astraea is one of the 3 main Angeloid's. She is often represented as dumb.
In Greek Mythology, Astraea, also called Astraia, is the virgin Godess of Justice.
We can link the character and the Godess by the innocence implied by the fact that Astraea, by her virginity, represents innocence, which is represented in Sora No Otoshimono by Astraea's stupidity and innocence.
Chaos is the first Angeloid of the second generation.
Chaos, in Greek Mythology, is the first thing that ever existed. More generally, it is often used to represent a gap, a void.
In SnO, Chaos is deeply searching for the meaning of love, and doesn't seem to understand what it means until the very end. This lack of love can be interpreted as a void, linking the character to the mythological notion. One also notices that the SnO Chaos' wings are pretty similar to some representations of the God.
In SnO, Chrysaor is Astraea's sword. It is referred to as the best weapon ever created for close-combat.
Chrysaor is the son of Poseidon and Medusa. The literal English translation of his name is "He who has a golden sword".
In SnO, Harpies are antagonists. They follow their master's orders until the very end. They are often cruel even though they almost fall in love in the Harpies' arc. They are sent by the Master of the Synapse to kill Ikaros as she had disobeyed her original master.
In Greek Mythology, a Harpy is a winged creature with a human face. They were created by Zeus to go to Earth and punish King Phineus.
Both the mythological creatures and the SnO's characters were sent down as a cruel response to what could be called an offense to the Gods.
Hiyori and Demeter
Demeter is the Goddess of harvest, the cycle of life, death and the seasons.
Hiyori is a reference to this Goddess in some points :
She is doing agricultural work, helping her parents to cultivate vegetables, therefore serving as a link with the agricultural Goddess
Her weapon, Demeter, can manipulate time, just as the greek Demeter would be able to manipulate seasons.
Ikaros, Daedalus and Minos
Those 3 characters are linked by the myth of the Labyrinth and Icarus' wings
Daedalus built the labyrinth for King Minos, who needed it to imprison his wife's son the Minotaur. The story is that Poseidon had given a white bull to Minos so that he might use it as a sacrifice. Instead, Minos kept it for himself; and in revenge, Poseidon made his wife Pasiphaë lust for the bull with the help of Aphrodite, who will later give birth to the Minotaur.
Minos imprisoned Daedalus himself in the labyrinth because he gave Minos's daughter, Ariadne, a clew(or ball of string) in order to help Theseus, the enemy of Minos, to survive the Labyrinth and defeat the Minotaur.
Daedalus fashioned two pairs of wings out of wax and feathers for himself and his son. Daedalus tried his wings first, but before trying to escape the island, he warned his son not to fly too close to the sun, nor too close to the sea, but to follow his path of flight. Overcome by the giddiness that flying lent him, Icarus soared into the sky, but in the process he came too close to the sun, which melted the wax. Icarus kept flapping his wings but soon realized that he had no feathers left and that he was only flapping his bare arms, and so Icarus fell into the sea in the area which today bears his name, the Icarian Sea near Icaria, an island southwest of Samos.
Hereafter the similar naming of the characters, there are some similarities :
- Ikaros has wings, like Icarus
- In SnO Daedalus is Ikaros' creator, as in Greek Mythology Daedalus is Icarus' father.
- In SnO Daedalus is forced to exile and Ikaros is sealed, as in Greek Mythology Daedalus and Icarus are jailed in the Labyrinth.
- Sugata always wishes to fly in order to discover the New World, which is a reference to this myth
- A reference to Icarus' fall is made in the final arc :
In the final arc, Ikaros reveals that she was previously ordered to destroy the Synapse. Even though they managed to control it, a security measure was taken : if Ikaros ever flew back to the Synapse without permission, she would be set on fire.
Here is another approach on Icarus myth which is not verified and mostly based on my deductions :
SnO may be intended as a reversed Icarus myth. The Icarus myth moral is
Humans should never try to achieve the dream of getting at the same level as Gods
And the moral of Sora No Otoshimono is
Because they have everything, Gods are inferior to humans as they, therefore can't dream.
Nymph is the second Angeloid to appear.
In Greek Mythology, different from other Goddesses, Nymphs are generally regarded as divine spirits who animate nature, and are usually depicted as beautiful, young nubile maidens who love to dance and sing.
Beta is known for loving nature, birds, and singing. On this points, she is quite similar to the mythological creatures.
What's more, a recurrent joke of Sora No Otoshimono is Nymph's little sized breast. In Greek Mythology, nymphs are sometimes represented in the shape of young maidens, which may explained the low developed secondary sexual characters of Nymph.
In SnO, Oregano is one of the medical Angeloids.
In real life, Oregano is a healing plant. In Greek Mythology, the Goddess Aphrodite invented the spice, giving it to man to make his life happier. The word "oregano" is actually derived from the Greek phrase, "joy of the mountains".
In SnO, the Pandora Mode is a second state mode of Angeloids where all their capabilities are hugely improved.
In Greek Mythology, Pandora is the first woman ever created.
Zeus ordered Hephaestus to create her. So he did, using water and earth. The Gods endowed her with many gifts: Athena clothed her, Aphrodite gave her beauty, Apollo gave her musical ability, and Hermes gave her speech.
According to Hesiod, when Prometheus stole fire from heaven, Zeus took vengeance by presenting Pandora to Prometheus' brother Epimetheus. Pandora opens a jar containing death and many other evils which were released into the world. She hastened to close the container, but all of the contents had escaped except for one thing that lay at the bottom – Elpis (usually translated "hope", though it could also mean "expectation").
I didn't find any relevant link between the Myths and the SnO mode.
In SnO, Poseidon is Minos' weapon.
In Greek Mythology, Poseidon is one of the 12 Gods and is called the "God of the Sea".
He carries a weapon, the Trident.
The Minos' weapon is clearly a reference to Poseidon's trident.
It is funny to mention that in the Myth, Poseidon punished King Minos for keeping a sacrifice for himself (See Ikaros, Daedalus and Minos entry)
Seiren appears very shortly in SnO before being killed by Chaos.
Sirens were beautiful and dangerous creatures who lured nearby sailors with their enchanting music and voices to shipwreck on the rocky coast of their island.
Seiren is an Angeloid designed for swimming, unlike other Angeloids, who do not float (due to the weight of their wet wings), therefore, serving as a link with Sirens which are always in the sea.
Uranus Queen (Ikaros)
Uranus is the Greek God of the sky. As Ikaros is the most powerful Angeloid ever created, the link is pretty obvious.
In SnO, Zeus is a weapon created to protect the Synapse against aggressors.
In Greek Mythology, Zeus is the sky and thunder God, ruling the other Gods.
They are linked as both throw thunderbolts and are in the sky