$B$-SCROLLS
WITH NON-DIAGONALIZABLE
SHAPE OPERATORS

DONG-SOO KIM AND YOUNG HO KIM

Abstract:

We study some Lorentzian surfaces in the three-dimensional Lorentzian space forms whose shape operators are not diagonalizable at least at one point. It is related to the so-called notion of 2-type surfaces. A local classification theorem in this respect is obtained.