<i>δ</i>(2,2)-Invariant for Lagrangian Submanifolds in Quaternionic Space Forms

Abstract

In the geometry of submanifolds, Chen inequalities represent one of the most important tool to find relationships between intrinsic and extrinsic invariants; the aim is to find sharp such inequalities. In this paper we establish an optimal inequality for the Chen invariant δ ( 2 , 2 ) on Lagrangian submanifolds in quaternionic space forms, regarded as a problem of constrained maxima.

Keywords

• <i>δ</i>(2,2)-invariant
• Chen inequalities
• Lagrangian submanifolds
• quaternionic space forms
• complex space forms