Hmmm, martial arts.
I doubt in a lot of the societies that there would be none outside the military.
Most of the current ones we have is from the military or from a time and a space in a society where technological advancement had plateaued and certain classes of people were not allowed to arm themselves.
Main reason for people learning them through the ages has been to protect oneself from bandits, robbers and other malcontents. If a society would reach a balance where the security forces and societal indoctrination would eradicate infighting within the population, the need for any martial arts would be eradicated.
In a thousand years of peace within a population you would have nothing left except dueling and physical culture exercises among the lines of yoga or chi-gong outside the military.
Let's see the Empires of New Eden and their characteristics.
One tribal.
Some Native American tribes did not even know how to hit people when they encountered the barbaric westerners. Their 'warfare' was based on 'counting coup' by touching the opponent with a long stick or with a painted hand.
Tribal warriors usually consider personal development and achievements to be the primary way of showing you how to be good at what you do. Therefore a tribal society would reject any formal way of training as something that would take away from that aspect of personal development. Modifying hunting skills for raiding neighboring tribes, using speed and wits to outsmart/maneuver the opposition to steal something of value. Avoiding loss of life being quite essential in the whole conflict, because if a hunter dies in a hunter-gatherer society then their family dies.
No wonder they were steamrolled by the Amarrians.
One communal.
After the collapse the terraforming was not finished. The whole society was confined to limited resources. Survival of the many was more important than the survival of the individual. After the terraforming was finished the population spread out forming small collectives, going through a tribal phase and later united into a one big collective.
In all likelyhood the whole society went through lengthy periods of peace and security. Causing less and less need for any kind of violence outside of the old military traditions.
No wonder they were steamrolled by the Gallenteans.
One fractional.
The kingdoms of Gallente prime in all likelyhood took pretty much very similar path that Europe did while they climbed from the post-collapse division of the population to the Federation. Constant civil war through millennia turned the population into individuals that sought be skillful enough to protect what was theirs. Even after the Federation was formed, the smaller states within the Gallentean population were in constant state of upmanship against the others when it comes to martial skills and technology.
Probably the most likely to have wide range of different martial arts traditions outside of the military, probably the most aggressive of the all Empires.
One religious.
After the collapse there were three factions on Athra. Two of them religious, Khanid and the Amarrians. Third the more technologically oriented Udorians. All three populations grew, Amarrians met the Khanid, Khanid had similar religion, joined the Amarrians. They kicked Udorian butt. Nature of the Scriptures basically states 'Never forget.' The military traditions that rose in the civil war became something to be revered and upheld. The nature of their religion proved to be right, when they came across other races and steamrolled them. Constantly adding more and more information about warfare into their Scriptures, learning from them, studying them, becoming more and more adept with them. Because of the nature of the society, martial arts outside the military completely unheard of. Ways of controlling the livestock, on the other hand. Quite common.
So, I would hazard a theory that there are roughly three types of martial arts in the cluster.
Military based, where you utilize all means necessary to kill the opponent. Weapons, no weapons.
Traditional, esoteric rules on conducting the conflict, even more esoteric rules about determining the victor.
Utilitarian, greatest amount of pain possible with minimum amount of permanent damage. Fast takedowns without permanent damage. Using the superior strength of the opponent against them.
As I stated before, I believe that very few would actually have any martial arts training.
Only third of the schools for the capsuleers in any Empire is military.
Usually any kind of military specialist training does not entail any hand to hand training, unless it is for a specialty where such training is needed. Wasting resources on teaching pilots to know how to have fisticuffs is wasted resources. Militaries work on efficiency.
I guess that pretty much sums up my current thoughts on the matter for the time being.