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Ali Taghavi
Ali Taghavi
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A polynomial function on the space$\mathbb{R}^3$ whose all level sets are mutually non isometric Riemannian manifolds

Is there a polynomial function $P: \mathbb{R}^3 \to \mathbb{R}$ with the following property?:

P does not have any critical value and for all $c \neq c'$, $f^{-1}(c)$ and $f^{-1}(c')$ are non isometric Riemannian manifolds(with the metric they inherit from the standard metric of $\mathbb{R}^3$)

A polynomial function on the space whose all level sets are mutually non isometric

Is there a polynomial function $P: \mathbb{R}^3 \to \mathbb{R}$ with the following property?:

P does not have any critical value and for all $c \neq c'$, $f^{-1}(c)$ and $f^{-1}(c')$ are non isometric Riemannian manifolds(with the metric they inherit from the standard metric of $\mathbb{R}^3$

A polynomial function on $\mathbb{R}^3$ whose all level sets are mutually non isometric Riemannian manifolds

Is there a polynomial function $P: \mathbb{R}^3 \to \mathbb{R}$ with the following property?:

P does not have any critical value and for all $c \neq c'$, $f^{-1}(c)$ and $f^{-1}(c')$ are non isometric Riemannian manifolds(with the metric they inherit from the standard metric of $\mathbb{R}^3$)

Source Link
Ali Taghavi
Ali Taghavi
  • 366
  • 8
  • 31
  • 123

A polynomial function on the space whose all level sets are mutually non isometric

Is there a polynomial function $P: \mathbb{R}^3 \to \mathbb{R}$ with the following property?:

P does not have any critical value and for all $c \neq c'$, $f^{-1}(c)$ and $f^{-1}(c')$ are non isometric Riemannian manifolds(with the metric they inherit from the standard metric of $\mathbb{R}^3$