In what manner / How, did Hashem appear to Avraham at Mamre? (Gen 18:1)
We read in Gen 18:1 וַיֵּרָא אֵלָיו יְהוָה, בְּאֵלֹנֵי מַמְרֵא; וְהוּא יֹשֵׁב פֶּתַח-הָאֹהֶל, כְּחֹם הַיּוֹם.
And Hashem/The LORD, appeared to him by the oaks/terebrinths of mamre, and he sat by the opening of the tent during the heat of the day.
We see then three men (Shlosha Anashim), approach Avraham(18:2). In v22 The men leave, Avraham continued standing before Hashem.
Hashem says he will go down (To sodom). Also(v23) Avraham drew near(to the LORD/Hashem), and he spoke to him.
So I don't think anybody can claim based on the text, that God appeared in any human form, and judaism doesn't make that claim so that's fine. Furthermore, while Avraham does bow to the ground to greet the men(vayishtechu artzah v2), so too David bows like that to Jonathan(artzah vayishechu) 1 Sam 20:41. So one can't read too much into a bow or such a bow. i.e. the bow doesn't indicate that the men are God in any way, though they are perhaps messengers from God.
And afterwards, (v33) Hashem went.. ..וַיֵּלֶךְ יְהוָה
But it does leave open the question - in what manner did God appear to Avraham?
So Hashem had not yet come down to Sodom. And assuming he hadn't come down, then it seems he appeared to Avraham in a vision. If so, do we have any traditions about what that vision was?
Or just generally any traditions or opinions on the nature of this appearance that Hashem made to Avraham?
Note- There is something else that I had not noticed before. And it may also explain why some rabbinical commentators consider this to be a vision rather than a literal event. (note, Gen 18 and Gen 19 have a good selection of variations of Adonai to look at), When there is a kamatz on the nun of ADNY, it's a name, a proper noun, for Hashem. (Putting ADNY aside for a moment), many translations distinguish things well with the word Lord/LORD/lord(s), by writing LORD for the tetragrammaton, (back to ADNY), Lord for Adonai with a kamatz. There is ADNY with a patach, adonay (lords), which is rare. And adonee for my lord. So the English distiguishes very clearly with the capital l, LORD, and Lord and lowercase 'l', lord(s). (And of course God and gods for elohim). Given that, there are two things here..
The main thing I recently noticed in Gen 18, is the kamatz on Adonai, so a man(or what was referred to as a man), is addressed with Adonai(with kamatz).
The other thing, which I don't think is that significant I couldn't find a Jewish link listing all the tikkunei sofrim(emendations of the scribes), but these links https://levendwater.org/companion/append32.html http://www.oocities.org/hebrew_roots/html/hr-2-1-02.html mention 134 compiled by Ginsberg, and Gen 18:3 is one, where according to those links, the tetragrammaton was changed to Adonai(i.e. Adonai with kamatz) it's not that significant in terms of meaning because it still means the same thing, Lord with a capital L, be it LORD(the tetragrammaton) or Lord(the name, Adonai with a kamatz).
Another thing I hadn't noticed is in Gen 19:1, it says 2 messengers came to sodom. That suggests that in the earlier Gen 18:22 when it said the men left to sodom, it was only two that left, and one remained.