MODERN TOPICS IN SUBMANIFOLD THEORY

The present book deals with the theory of Chen invariants, a very modern topic in Submanifold Theory, initiated in 1993 by Prof. B. Y. Chen. He translates some problems of the world into mathematical problems.
Almost everyone desires to live in a “best world” without tension from the surrounding space. By a “best world” we mean “a surrounding space which has the highest degree of homogeneity at every point”. The question is whether “to live in a best world without tension” is a real possibility.
This monograph could be a graduate course for Master students and Ph. D. students in Differential Geometry. It introduces them in a new and interesting research topic: relationships between intrinsic invariants and extrinsic invariants of submanifolds, via Chen invariants, and answers to basic problems in Submanifold Theory. Also, it is useful to professors and researches in Differential Geometry and Submanifold Theory, as well as to physicists and applied mathematicians, by the applications of Chen inariants in other branches of Mathematics and other sciences.