Özet:
The aim of this thesis examine some properties of complete maximal spacelike surfaces
in the Anti de-Sitter space.
In the first and second chapter, Historical improvement about Anti de-Sitter space and
fundemental definitions and theorems are given.
In the third chapter, some properties of complete maximal spacelike surfaces in the Anti
de-Sitter space and square of the norm of the second fundamental form are examined.
For this aim is considered Anti de-Sitter space such that size and an index of two with
constant curvature. First of all, to obtain required results fundemental concepts about
the topic are considered and the studies about anti de-Sitter space are investigated.
On the result of these, the relation between complete maximal spacelike surface 2 M
with the constant curvature c in the anti de-Sitter space 4
2 H c( ) and the second
fundamental form S is found such that 2 M surface is the total geodesic surface and
hyperbolic Veronese surface, respectively if and only if S 0 and 4
3
c S , and the
space 4
2 H c( ) is hyperbolic cylinder the total geodesic surface of 3
1 H c( ) if and only if
S c 2 .
