Ṛshyamūka Parvata is the mountain near Lake Pampā where the vānara king Sugrīva lived after his elder brother Vāli drove him out of Kishkindhā. The mountain was guarded by a śāpa (a curse) laid by a muni, and Vāli could not set foot on it without being harmed. This made it Sugrīva’s only safe refuge. In the Āraṇya Kāṇḍa, both Kabandha and Śabarī sent Rāma to Ṛshyamūka to find Sugrīva. As Rāvaṇa carried Sītā away, she dropped her jewels onto the slopes of what the tradition understands to be this mountain. The vānaras found them there and later brought them to Rāma.

Sugrīva’s refuge

Ṛshyamūka was the one place in the world where Vāli, the strong elder brother of Sugrīva, could not safely follow him. The śāpa of Mataṅga Muni, which came from the Dundubhi incident, made the mountain forbidden to Vāli. If he set foot on it, his head would split into a hundred pieces. This gave Sugrīva a lasting refuge from which he could not be driven out, however weak he was in other ways. He lived on Ṛshyamūka with a small band of faithful vānaras, among them Hanumān. The Vālmīki Rāmāyaṇa tells this in the Āraṇya Kāṇḍa, chapters 71 and 72, and in the Kishkindhā Kāṇḍa, chapters 11 and 12.

The scattered jewels

Rāvaṇa flew south in his pushpaka vimāna (flying chariot) with Sītā. She threw down her jewels as signs for Rāma. They fell on the slopes of a hill or mountain in the south, which the tradition understands to be Ṛshyamūka. The vānaras who lived there found them. Later Rāma and Lakshmaṇa came and described Sītā, and the vānaras knew the jewels again. They were proof that Rāvaṇa had flown this way. The Vālmīki Rāmāyaṇa tells this in the Āraṇya Kāṇḍa, chapter 48.

The counsel to go there

Kabandha, freed from his curse by Rāma, and Śabarī at her āśrama both told Rāma to go to Ṛshyamūka, to seek Sugrīva there and make him an ally. So Ṛshyamūka was not only a place of exile. It was the appointed meeting place where Rāma’s task would find its needed partner. The Vālmīki Rāmāyaṇa tells this in the Āraṇya Kāṇḍa, chapters 71 to 75.

Sources

Vālmīki Rāmāyaṇa, Āraṇya Kāṇḍa, chapters 48 and 71–75
Vālmīki Rāmāyaṇa, Kishkindhā Kāṇḍa, chapters 11–12