Authors: Abhitosh Upadhyay

DOI: 10.24064/iwts2016.2017.12

Abstract: In this paper, we present a short survey about recent results on biconservative hypersurfaces in pseudo-Riemannian space forms and discuss some open problems on this topic. Further, we consider canonical forms of the shape operator of biconservative hypersurface of index 2 in $\mathbb E^5_2$ and by choosing an appropriate base field, we obtain that there are six possible canonical forms of the shape operator satisfying $\langle\nabla H, \nabla H\rangle = 0$, i.e., $\nabla H$ is light-like vector.

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