Pseudo-Symmetries of Generalized Wintgen Ideal Lagrangian Submanifolds

Miroslava Petrović-Torgašev, Anica Pantić

Abstract: Mihai obtained the Wintgen inequality, also known as the generalized Wintgen inequality, for Lagrangian submanifolds in complex space forms and also characterized the corresponding equality case. Submanifolds $M$ which satisfy the equality in these optimal general inequalities are called generalized Wintgen ideal submanifolds in the ambient space $\tilde{M}$. For generalized Wintgen ideal Lagrangian submanifolds $M^n$ in complex space forms ${\tilde{M}}^n\left(4c\right)$, we will show some properties concerning different kinds of their pseudosymmetry in the sense of Deszcz.

Keywords: generalized Wintgen ideal submanifold, pseudosymmetric space, Lagrangian submanifold, complex space form

Classification (MSC2000): 53C40; 53C25

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