Metric tensor notation for spacetime interval in Euclidean space-time

[member 141513]

In Euclidean Space-Time, the kinematic equation is:
$$s^2=g_{\mu\nu}x^{\mu}x^{\nu}$$
am i correct if i write :
$$K^{\mu \nu}_{\mu \nu}=g_{\mu \nu}x^{\mu}x^{\nu}$$
where $$s^2=K^{\mu \nu}_{\mu \nu}$$?
thank you very much

 

[Meir Achuz]

You could, but why? You do understand that the repeated indices mean a sum over all mu and nu from 0 to 3.