In combining contact improvisation and tantra in my teaching one of my focuses is:

Breathing:

1. How breathing can support a (CI) dancing:

For example a start with arm swings:
In standing, swing the arms up over the head with breathing in and swing them down und a bit behind you with the breathing out. Use bending and opening of your knees for that arm swing, so that the knees are open, when the arms are up, they bend all the way you swing the arms down and get longer again, when you swing the arms behind you. This creates a wave along the spine in the body. Breathing in swinging the arms up, opening the upper body. Breathing out  swinging the arms down and behind, you are closing the upper body to the front and make a round spine. You can feel the opening and extending of the torso and the whole body with breathing in. The movement produceses a wave in the body along the spine, which is important in tantra (to let energy move up along the spine).
Doing that about 10 min.

As a solo improvisation finding movemets of opening/extending the body with breathing in and of closing/ making smaller in breathing out. You can make the breath much bigger than normal breathing.
Second step: Exploring with movements get supported by breathing in and which by breathing out.

An exercise for advanced would be to go into a duo with that link of breathing and dancing in listening to each other and finding a dance together first touching each other not physically, later also with physical touch and giving a bit of your weight. Synchronization of the breath can happen. It can happen that you breath in and out together for a while or that your partner is breathing in, when you breath out.

Another solo exploration:
Move with breathing in, extending into the space, stop moving with breathing out. Sensing the group around you in the stop.

Another solo exploration:
Move with breathing out, stop moving with breathing in. Sensing the group around you in the stop.

Duo with an other partner: Move with breathing in, extending into the space, stop moving with breathing out. Start without physical touch, later also with physical touch and giving of weight. Listening to your breath and movement and the breath and movement of the other. Synchronization of the breath is welcome, so you can find the stops and the coming into movement again together.

Another solo exploration:
Dance while you are breathing and let the breath support the dance and from time to time find a stop of the moving and don’t breath. Feel the space and the others around you and how you get touched by them or how you touch them especially in the stop (without physical touch). Play with the rhythm of the movement and the stops.

Another solo exploration:
Dancing during you are not breathing and stop the movement while you are breathing.Play with the rhythm and sound of the movement. Feel the space and the others around you and how you get touched by them or how you touch them especially in the stop (without physical touch).

Duo with an other partner: Finding a dance together in listening to each other and the sound and rhythm of your own and your partner’s movements. Let the breathing support your movement and dance. Find stops together, where you both don’t breath. See how long or short that stop can be. Find into movement together after the stop.
Start without physical touch and come later into physical touch and giving of weight to your partner or taking of the weight of your partner.

Duo with another partner:
In listening to the breath and the sound of the movements of yourself and your partner find a dance together. Find stops, silence in that dance together. Play with the duration of these stops. You can have physical contact and also no physical contact for a while and play with the distance to each other.

2. Breathing in as opening, width that gives you lightness in the dance

3. Breathing exercises for each chakra (energetic center in the body). Specific breathing exercises for the three layers of pelvic floor musles and how these exercises can be useful for dancing

3. Belly breathing combined with rocking movement of the pelvis (important in tantra)
“Get a good sitting position, feeling your sitting bones. Have a good connection down, extended into the floor/the earth, extendes, reaching into the earth and good connection up, extended, reaching towards the universe. There is a long vivid spine, which a lot of potential for movement. Place one hand on the lower belly hand between your navel and the pubic bone and the other one the sacrum. That one better with the back of the hand on the sacrum, for this feels more easy for the arm). Sense into the space under your hands, the pelvis. See, if you can reach that space with your breath, so that the lower belly gets wide, extends with the breathing in. Feel the sensations, energies, warmth, emotions  under your hands. With the breathing in move the pelvis in your hand in front and with the breathing out in the hand on the sacrum. A rocking movement of the pelvis tales place.

After a while:  The rocking movement of the pelvis generates a wave through the spine with the breathing in , if you let your spine freely react to the rocking movement of the pelvis. You can imagine to breath in from the perineum, pelvis, genitals and let then the breathing in widening the ripcage and let the sternum rise. So the breathing in reaches the space of the hearth. With the breathing out the sternum sinks, the ripcage gets smaller, you move backwards from the sacrum und lower lumbar spine and can imagine to breath out from the perineum (and  if you want from the genitals).“

4. Connecting the pelvis with the heart (important in tantra), for example through the breathing

5. Tantric breathing circles in the body