Some curvature conditions of the type $4\times2$ on the submanifolds satisfying Chen's equality

Abstract

Submanifolds of the Euclidean spaces satisfyingequality in the basic Chen's inequality have, as is known, manyinteresting properties. In this paper, we discuss the curvatureconditions of the form $E\cdot S=0$ on such submanifolds, where$E$ is any of the standard 4-covariant curvature operators, $S$is the Ricci curvature operator, and $E$ acts on $S$ as aderivation.