As Hindu and Buddhist religions came to influence Asiatic culture the martial arts aspects were also shared, included in this is the role of dance and martial art. Many cultures in Asia have dances today that appear to relate to this era.
Here is a Sword Dance from Thailand:

it is easy to see how a dance serves the same purpose as form and kata, while remaining often more formal and incorporating elements of timing and expression in a way that Kata and form cannot easily encompass.
Here is another martial dance from Thailand used in Muay Thai:


It has many common elements with Indian dancing as do many Thai dances. Some Thai dances even depict Shiva with masks and Bharata, the sage who wrote the Indian classic on performance art which states that the dances are as martial as they are entertaining, and spiritual as well. Note how the postures of the fighters in the video above are somewhat reminicent of the Dancing Shiva, Lord Nataraja.