Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants

One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds. In order to establish such relations, the first author introduced in the 1990s the notion of delta-invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on delta-invariants and their applications have been summarized in the first author's book published in 2011 Pseudo-Riemannian Geometry, delta-Invariants and Applications (ISBN: 978-981-4329-63-7). In this survey, we present a comprehensive account of the development of the differential geometry of submanifolds in complex space forms involving the delta-invariants done mostly after the publication of the book.