First I will explain my motivation to introduce the ?-invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of ?-invariants in several areas in mathematics. Finally, I will present two optimal inequalities involving ?-invariants for Lagrangian submanifolds obtained very recently in joint papers with F. Dillen, J. Van der Veken and L. Vrancken.
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Bang‐Yen Chen (2013) studied this question.
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