ON SUBMANIFOLDS SATISFYING CHEN'S EQUALITY IN A REAL SPACE FORM

摘要

In [1], B.-Y. Chen recalled that one of the basic interests of submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of a submanifold. The main extrinsic invariant is the squared mean curvature and the main intrinsic invariants include the classical curvature invariants, namely the scalar curvature and the Ricci curvature, and the well known modern curvature invariant, namely Chen invariant [2].