A tour through $\delta$-invariants: From Nash's embedding theorem to ideal immersions, best ways of living and beyond

Abstract

First I will explain my motivation to introduce the $\delta$-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 $\delta$-invariants to several areas in mathematics. Finally, I will present two optimal inequalities involving $\delta$-invariants for Lagrangian submanifolds obtained very recently in joint papers with F. Dillen, J. Van der Veken and L. Vrancken.

arXiv comment14 pages, to appear in a special volume of Publications de l'Institut Mathematique, Proceeding of XVII Geometrical Seminar, September 3-8, 2012, Zlatibor, Serbia