MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Some curvature conditions of the type $4\times2$ on the submanifolds satisfying Chen's equality
Miroslava Petrović-Torgašev and Ana Hinić

Abstract

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.

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Keywords: Submanifolds, curvature conditions, basic equality.

MSC: 53B25, 53C40

Pages:  143$-$150     

Volume  59 ,  Issue  3 ,  2007