Some curvature conditions of the type 4x2 on the submanifolds satisfying Chen's equality

Miroslava Petrović-Torgašev, Ana Hinić

Submanifolds of the Euclidean spaces satisfying equality in the basic Chen's inequality have, as is known, many interesting properties. In this paper, we discuss the curvature conditions 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 a derivation.