Biharmonic Hypersurfaces in the Pseudo-Euclidean Space E^5_2
2019
Ruya YEGIN SEN
In this work, biharmonic hypersurfaces of index 2 in pseudo-Euclidean space are studied under the assumption of having mean curvature H whose gradient NH is light-like, i.e. hNH;NHi = 0 and NH 6= 0. In the first two sections, the problem is introduced and some basic definitions and formulas that we will use in other part of the paper are recalled. Moreover, all possible canonical forms of the shape operator of a hypersurface of index 2 are obtained. In the third section of this work, for each of these cases, some of geometrical properties of hypersurfaces is investigated. In particular, there are 2 possible canonical forms of the shape operator for a biharmonic hypersurface such that whose gradient NH is light-like are obtained. After that, the non-existance of biharmonic hypersurface of index 2 in pseudo-Euclidean space E52 with the light-like NH is proved. In the last section, the results from this work is summarized and the discussion part is given.
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