Let \(M=\{z\in \mathbb {C}^n=\mathbb {R}^{2n}:z_1^2+\cdots +z_n^2=1\}\). Prove that \(M\) is a regular submanifold of \(\mathbb {R}^{2n}\), and find it’s dimension.
Question
Math 6510 • Differentiable Manifolds
Spring 2008 • Question 1
Question
Spring 2008 • Question 1
Let \(M=\{z\in \mathbb {C}^n=\mathbb {R}^{2n}:z_1^2+\cdots +z_n^2=1\}\). Prove that \(M\) is a regular submanifold of \(\mathbb {R}^{2n}\), and find it’s dimension.