Is Aang related to Korra?

Question

Except for being the incarnation of Aang, is Korra related to him also by blood?

Is it said anytime during the show?

Answer 1

They are not related, but there might be family relations anyway.

It is never said during the show, and you can see many family trees that show there is no connection except for being the incarnation of each other as you said (blue line connection):

However, the possibility exists.

Since both Korra and Katara were born in the Southern Water Tribe, and since the water tribe was very thin during the first show, as you can see from S01E01, when Katara introduce the "entire tribe" as she said, to Aang:

There are only 21 people in the tribe (with Katara and Sokka, not in the picture), and Katara said all the men left for the war, so if those are all the women and children, there are probably less than 10 men. so the chances that Korra's mother is related to Katara somehow is a possibility. (her father is originally from the northen tribe).