*Article δ***(2, 2)-Invariant for Lagrangian Submanifolds in Quaternionic Space Forms**

**Gabriel Macsim 1,†, Adela Mihai 2,† and Ion Mihai 3,\*,†**


Received: 27 February 2020; Accepted: 23 March 2020; Published: 1 April 2020

**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:** *δ*(2, 2)-invariant; Chen inequalities; Lagrangian submanifolds; quaternionic space forms; complex space forms

**MSC:** 53C40; 53C25
