Bu y¸ksek lisans tezi ¸Á bˆl¸mden olu¸smaktad¨r.
Birinci bˆl¸mde bu Áal¨¸smada kullan¨lacak olan temel kavramlar tan¨mland¨ve ilgili teoremler verildi.
Ikinci bˆl¸mde regle y¸zey ve ikinci Gauss e · grili º gi tan¨m¨verilerek Minkowski º
uzay¨nda regle y¸zeyin ikinci kuadratik formu ve Riemann veya Pseudo
Riemann manifoldunun ikinci Gauss egrili º ginin matris gˆsterimi elde edildi. º
‹Á¸nc¸ bˆl¸mde ise Young Ho Kim, Dae Won Yoon taraf¨ndan yap¨lan
[4] nolu Áal¨¸sma ayr¨nt¨l¨olarak incelenmi¸stir. Ayr¨ca 3-boyutlu R
3
1 uzay¨nda
regle y¸zeylerin ikinci Gauss egrili º gi º KII incelendi. H ortalama egrilik º
a; b 2 R olmak ¸zere aKII + bH = sabit ise regle y¸zey helicoid, KII = 2H
ise canoid oldugu gˆsterildi ve bunlar s¨n¨áand¨r¨ld¨.
This thesis contains three chapters.
In the Örst chapter, we give fundamental deÖnitions and some theorems
that it needs for our study.
In the Second chapter, we obtained the second Gaussian curvature. In
addition, we obtained second gaussian curvature of matrix representation on
Pseudo-Riemannian manifold.
In the third chapter, we have studied the study of by Young Ho Kim, Dae
Won Yoon [4]. In addition we have study of the second Gaussian curvature
KII of ruled surfaces in the 3- dimensional space R
3
1
. It has been showed that
if aKII +bH, a; b 2 R; is a constant then the ruled surface is a helicoid and if
KII = 2H then it is a conoid. Where H is the mean curvature. Furthermore
the helicoid and conoid have been classiÖed.