Lagrangian submanifolds with prescribed second fundamental form

2013/09/17 by Chen, Bang-Yen, Van der Veken, Joeri, Vrancken, Luc
#Differential Geometry (math.DG) #Differential geometry #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4365

Abstract

We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of this parameter, the resulting submanifolds are ideal in the sense that they realize equality in an inequality for a Chen's delta-curvature.

Related

• Classification of δ(2,n-2)-ideal Lagrangian submanifolds in n-dimensional complex space forms
• δ-invariants for Lagrangian submanifolds of complex space forms
• Curvature inequalities for Lagrangian submanifolds: the final solution
• Chen's inequality in Lagrangian case
• Lagrangian submanifolds in para-complex Euclidean space