Question

Dirichlet's work on gravity in non-Euclidean space?

Answer 1

In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514):  "The German mathematician Lejeune Dirichlet studied the law of gravitation in non-Euclidean space towards the end of 1850."  Does anyone perhaps know more about that?

Answer 2

 correct interpretation of T=Tx+Ty+TzT=Tx+Ty+Tz and whether is it possible to have a "manifold" where such a Pythagoras like theorem exists that one can write say, T=Tx+Ty−TzT=Tx+Ty−Tz –