All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, what you mentioned about the Prophet that when he prayed he would incline his head and fix his sight towards the ground, is not authentically reported from him; rather this narration about him is weak.
As regards the narration “His sight did not leave the place of his prostration while he was in the Ka’bah”, then this is an authentic narration. It is also confirmed authentic that he said: “There should not be in the House anything which may disturb the praying person”. However, these two narrations do not prove that one should look at the place of prostration during the prayer.
It is for this reason that the jurists differed in opinion about the place where the praying person should look at when performing the prayer. Some of them stated that it is desirable for the praying person to look at the place of prostration when he is standing in prayer, to look at his feet when he is in the bowing position, to his nose when he is in the prostration, and to his lap when sitting in Tashahhud. However, some other scholars stated that it is desirable for the praying person to look at the place of prostration during the whole prayer, yet others had different opinions.
Allaah Knows best.