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## Main Question or Discussion Point

Hi there, i have a lot of question about Lorentz-Minkowski geometry:

we say that timelike subspaces include null and spacelike vectors and lightlike subspaces include

spacelike vector?

are timelike planes Sp{E

Sp{E

**Is Lorentz metric degenere or non-degenere? Why?**

1)1)

**2)**In spacelike subspaces only spacelike vectors live in it there is not problem here but how canwe say that timelike subspaces include null and spacelike vectors and lightlike subspaces include

spacelike vector?

**3)**Let E_{1}spacelike and E_{2}timelike vector then E_{1}+E_{2}is null vector, proof...?**4)**If Sp{E_{1},E_{2}} spacelike, Sp{E_{1},E_{3}} and Sp{E_{2},E_{3}}are timelike planes Sp{E

_{1},E_{2}+E_{3}} is lightlike plane?**5)**E_{1}+E_{2}+E_{3}is spacelike vector butSp{E

_{1},E_{1}+E_{2}+E_{3}} is lightlike plane?**6)**E_{2}+E_{3}is lightlike vector but Sp{E_{2}+E_{3},E_{3}} is timelike plane?