Generalized wintgen inequality for bi-slant submanifolds in locally conformal Kaehler space forms

Abstract

In 1999, De Smet et al.\ conjectured the generalized Wintgen inequality for submanifolds in real space forms. This conjecture is also known as the DDVV conjecture and it was proved by Ge and Tang. Recently, Mihai established such inequality for Lagrangian submanifold in complex space forms. In this paper, we obtain the generalized Wintgen inequality for bi-slant submanifolds in locally conformal Kaehler space forms. Further, we discuss the particular cases of this inequality i.e.\ for semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds, invariant submanifolds and anti-invariant submanifolds in the same ambient space.