A Generalization of Minimal Cones

Abstract

Let ${R_ +}$ be a positive real line, ${S^n}$ an $n$-dimensional unit sphere. We denote by ${R_+} \times {S^n}$ the polar coordinate of an $(n + 1)$-dimensional Euclidean space ${R^{n + 1}}$. It is well known that if $M$ is a minimal submanifold in ${S^n}$, then ${R_ +} \times M$ is minimal in ${R^{n + 1}}$. ${R_+} \times M$ is called a minimal cone. We generalize this fact and give many minimal submanifolds in real and complex space forms.