Kurma (कूर्म; , 'Turtle', 'Tortoise'), is the second avatar of the Hindu preserver deity, Vishnu. Originating in Vedic literature such as the Yajurveda as being synonymous with the Saptarishi called Kashyapa, Kurma is most commonly associated in post-Vedic literature such as the Puranas. He prominently appears in the legend of the churning of the Ocean of Milk, referred to as the Samudra Manthana. Along with being synonymous with Akupara, the World-Turtle supporting the Earth, Kurma is listed as the second of the Dashavatara, which are the ten principal incarnations of Vishnu.
The Sanskrit word 'Kurma' (Devanagari: कूर्म) means 'Tortoise' and 'Turtle'. The tortoise incarnation of Vishnu is also referred to in post-Vedic literature such as the Bhagavata Purana as 'Kacchapam' (कच्छप), 'Kamaṭha' (कमठ), 'Akupara' (अकूपार), and 'Ambucara-Atmana' (अम्बुचर-आत्मना), all of which mean 'tortoise' or 'form of a tortoise'.
Written by the grammarian Yaska, the Nirukta is one of the six Vedangas or 'limbs of the Vedas', concerned with correct etymology and interpretation of the Vedas. The entry for the Tortoise states (square brackets '[ ]' are as per the original author):May we obtain that illimitable gift of thine. The sun is called akupara also, i. e. unlimited, because it is immeasurable. The ocean, too, is called akupara, i. e. unlimited, because it is boundless. A tortoise is also called a-kupa-ara, because it does not move in a well [On account of its shallowness]. Kacchapa (tortoise) is (so called because) it protects (pati) its mouth (kaccham), or it protects itself by means of its shell (kacchena), or it drinks (√pa) by the mouth. Kaccha (mouth or shell of a tortoise) = kha-ccha, i. e. something which covers (chddayatl) space (kham). This other (meaning of) kaccha, 'a bank of a river', is derived from the same (root) also, i.e. water (kam) is covered (chadyate) by it.
As illustrated below, Vedic literature such as the Samaveda and Yajurveda explicitly state Akupara/Kurma and the sage Kashyapa are Synonymous.