IMPROVED CHEN’S INEQUALITIES FOR LAGRANGIAN SUBMANIFOLDS IN QUATERNIONIC SPACE FORMS

Abstract

Riemannian invariants (in particular Chen invariants) play an important role in the theory of submanifolds. They are very useful in providing relationships between the extrinsic and intrinsic invariants of a submanifold. On the other hand, Lagrangian submanifolds are one of the most studied, with important roles in other fields. In this paper, an improved inequality for the Chen invariant δ_M and an inequality for the invariant δ(n1, . . . , nk), both in the case of a Lagrangian submanifold in a quaternionic space form, by using an optimization method, are obtained.

Keywords

• delta_M invariant
• . . .
• nk) invariant
• delta(n_1;...;n_k) invariant