A generalization of minimal cones

Abstract

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