Recent developments in $\delta$-Casorati curvature invariants

Authors: BANG-YEN CHEN

Abstract: The theory of $\delta$-invariants, initiated by the author in the early 1990s, is a challenging topic in modern differential geometry, having a lot of applications. In the spirit of $\delta$-invariants, Decu et al. (2007) initiated the study of $\delta$-Casorati curvatures. Since then there are many interesting results on $\delta$-Casorati curvatures obtained by many authors. In this article we provide a comprehensive survey on recent developments in $\delta$-Casorati curvatures done during the last decade.

Keywords: $\delta$-invariant, Chen invariant, $\delta$-Casorati curvatures, Chen ideal submanifold, Casorati ideal submanifold, optimal inequality

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