Did Elvis meet tony curtis?

All I know for a fact is that Elvis admired Tony Curtis's hairstyle to the point of copying it earlier on in his career. They might have hit it off, sharing hobbies like chasing women, playing pranks and making music, though Tony only played the flute whereas Elvis could play piano, drums and guitar to accompany his golden voice. It's a pity that Elvis never really tried his hand at comedic acting, it might have suited his innate sense of humour and surely he could have learnt the ropes from Tony, who was second to none at this.