@ecterrab 

Hello!

Thank you for your answer: using "assuming positive" option gives just the answer I expected! Somehow I missed it completely. 

Will take your advice about transforming TeX to Maple in the future.

As for the reason I'm using DifferentialGeometry, I need to use LieAlgebras subpackage of it in the further calculations, so I kinda have to stick to it.

Thanks a lot once more, and have a nice day,

Nick

@ecterrab 

Thanks, it worked!

@Torre

That solved my problem. Should have noticed that I have only 4 non-zero diagonal terms for d=6 metric :)