Abstract
In the theory of submanifolds, the following problem is fundamental: es- tablish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udriste that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequal- ity which characterizes a totally real submanifold of a complex space form. For that we suppose that the submanifold is Lagrangian and we formulate and analyze a suitable constrained extremum problem.
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