Very similar to a Beast Master's Animal companion, the Geomancer gains the aid of a Geo Beast that aids it on and off the battlefield. Though the statistics are the same, the geo Beast is a bit different due to it's unique nature.
Animal companion: 
Geo Beast Edit
Size: Small; Speed: 30 ft.; Attack bite (1d4); Ability Scores: Str 12, Dex 15, Con 12, Int 2, Wis 12, Cha 5; Special Qualities: low-light vision.
Geo Assimilation (Su): A Geo Beast is in tune with the Geo Panel it possesses on it's back, and as such, it can gain and grant great power to those around him. The Geo Beast grants it's Geo Ability (Chosen from the Geo Panel Abilities below), to any creature standing within 5 feet of it. This increases by 5 feet for every 4 hit dice the creature possesses.
Ability Scores Str +2, Con +2.
Geo Boost (Su) As a standard action, a Geo beast can spread the radius of it's Geo Ability by 5 feet for every hit dice it possesses. This lasts until the end of your next round, and the Geo Beast cannot use this ability for 1d4 rounds afterward.
Ability Scores Dex +2, Con +2.
Selective Geography (Su) A Geo Beast can choose who is and isn't effected by the ability it grants.
NOTE: Once chosen, the ability cannot be changed. Abilities that allow you to specify a certain type, such as the weapon proficiency and the energy resistance, must be chosen at first level and cannot be changed. (I.E. If you choose Great sword proficiency as the Geo beast's power, it cannot be changed to a different weapon.) In addition, Geo Beasts always benefit from the ability of their geo panel.
Some DM's may allow a Geomancer to use some of the natural Geo Abilities, however they can be quite powerful and may require a feat. [wiki:disgaead20:"Geo Panel Abilities"]
If Reincarnating into this class after having already been this class, or a class with similar abilities, check the following page to see what ability you'll get instead at the levels you would normally gain an already achieved class ability.