The cosmic tortoise, and Mount Meru
The Kurma legend appears in the Vedic texts, and a complete version is found in the Shatapatha Brahmana of the Yajurveda..  Both Kurma and Matsya are exclusively and clearly linked to Vishnu.
Kurma in the Vedic texts is a symbolic cosmogonic myth. He symbolizes the need for foundational principles and support for any sustained creative activity. In sections 6.1.1 and 7.5.1 of the Shatapatha Brahmana, Kurma's shape reflects the presumed hemispherical shape of the earth and this makes it part of the fire altar design. He is also considered the lord of the waters, thus symbolism for Varuna. In these early Hindu texts, Varuna and goddess earth are considered husband and wife, a couple that depend on each other to create and nourish a myriad of life forms. Alternate names such as Kumma, Kashyapa and Kacchapa abound in the Vedic literature, as well as early Buddhist mythologies such as those in the Jataka Tales and Jain texts, which also refer to tortoise or turtle.
The Kurma legend is described in Vaishnava Puranas. In one version, sage Durvasa curses the Devas (gods) to lose their powers because they slighted him. The gods needed nectar of immortality (amrit) to overcome this curse, and they make a pact with the asuras (demons) to churn the cosmic ocean of milk, so as to extract the nectar, and once it skims out they would share it. To churn the ocean of milk, they used Mount Mandara as the churning staff, and the serpent Vasuki as the churning rope while the turtle Kurma, Vishnu bore the mountain on his back so that they could churn the waters so that the churning staff would not sink the cosmic waters.
The Asuras immediately took the nectar, and quarreled amongst themselves. Vishnu then manifested himself as the beautiful Mohini and tricked the Asuras to retrieve the potion, which he then distributed to the Devas. Though the Asuras realized the trick, it was too late—the Devas had regained their powers, and were then able to defeat their foes.