Final answer:
Amir Khusraw, a Hindu poet, was influenced by Islamic mysticism and incorporated its teachings into his works.
Step-by-step explanation:
The Hindu poet who was influenced by Islamic mysticism was none other than Amir Khusraw. Khusraw was a significant figure in the 13th century, known for his contributions to poetry, music, and mysticism. He was deeply influenced by Sufism, a mystical branch of Islam, and incorporated its teachings and themes into his works. Khusraw's poetry often expressed themes of divine love and spiritual awakening, reflecting the influence of Islamic mysticism on his Hindu background.