What is the name of repeated to and fro movement a horse over same ground in dressage?

The repeated to and fro movement of a horse over the same ground in dressage is called a "volte".

There are different types of voltes, such as:

* Half-volte: A semi-circular movement, typically ridden on a 10-meter circle.

* Full-volte: A full circle, ridden on a 20-meter circle.

* Serpentine: A series of half-voltes connected by straight lines.

* Counter-volte: A half-volte performed on the opposite rein.

Voltes are used to develop the horse's suppleness, balance, and responsiveness to the rider's aids.