IJPAM: Volume 36, No. 4 (2007)

MINIMAL SUBMANIFOLDS OF CONSTANT SECTIONAL
CURVATURE $C$ ISOMETRICALLY IMMERSED IN
A RIEMANNIAN SPACE FORM $R^{m}(c)$

Handan Yildirim
Department of Mathematics
Faculty of Science
Istanbul University
Vezneciler, Istanbul, 34459, TURKEY
e-mail: handanyildirim@istanbul.edu.tr


Abstract.The aim of this paper is to give some characterizations of a Riemannian $n$-manifold $M$ isometrically immersed in a Riemannian space form $R^{m}\left( c\right)$ of constant sectional curvature $c$ for the equality which involves $\widehat{\delta}$-invariant, the squared mean curvature of the Riemannian submanifold and $c$.

Received: February 1, 2007

AMS Subject Classification: 53C42, 53B20, 53C40

Key Words and Phrases: curvature, $\delta $-invariants, inequality, Riemannian space form

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 4