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Editing hopefully to clarify
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LSpice
LSpice
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Classification of "homogeneous" submanifolds of R^nℝⁿ

I define a subset $M$ of $\mathbb R^n$ to be a "homogeneous Euclidean Manifold"manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is ana Euclidean isometry $f$ of $\mathbb R^n$ sending $p$ to $q$ fixing $M$ (iei.e., $f(M)=M$ and $f(p)=q$). The problem is to classify the "homogeneous Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you

The problem is to classify the "homogeneous Euclidean manifolds".

I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case.

Classification of "homogeneous" submanifolds of R^n

I define a subset $M$ of $\mathbb R^n$ to be a "homogeneous Euclidean Manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is an Euclidean isometry $f$ sending $p$ to $q$ fixing $M$ (ie $f(M)=M$ and $f(p)=q$). The problem is to classify the "homogeneous Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you

Classification of "homogeneous" submanifolds of ℝⁿ

I define a subset $M$ of $\mathbb R^n$ to be a "homogeneous Euclidean manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is a Euclidean isometry $f$ of $\mathbb R^n$ sending $p$ to $q$ fixing $M$ (i.e., $f(M)=M$ and $f(p)=q$).

The problem is to classify the "homogeneous Euclidean manifolds".

I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case.

added 4 characters in body; edited title
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Andrea Aveni
Andrea Aveni
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Classification of "symmetric""homogeneous" submanifolds of R^n

I define a subset $M$ of $\mathbb R^n$ to be a "symmetric"homogeneous Euclidean Manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is an Euclidean isometry $f$ sending $p$ to $q$ fixing $M$ (ie $f(M)=M$ and $f(p)=q$). The problem is to classify the "symmetric"homogeneous Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you

Classification of "symmetric" submanifolds of R^n

I define a subset $M$ of $\mathbb R^n$ to be a "symmetric Euclidean Manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is an Euclidean isometry $f$ sending $p$ to $q$ fixing $M$ (ie $f(M)=M$ and $f(p)=q$). The problem is to classify the "symmetric Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you

Classification of "homogeneous" submanifolds of R^n

I define a subset $M$ of $\mathbb R^n$ to be a "homogeneous Euclidean Manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is an Euclidean isometry $f$ sending $p$ to $q$ fixing $M$ (ie $f(M)=M$ and $f(p)=q$). The problem is to classify the "homogeneous Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you
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Andrea Aveni
Andrea Aveni
  • 245
  • 1
  • 5

Classification of "symmetric" submanifolds of R^n

I define a subset $M$ of $\mathbb R^n$ to be a "symmetric Euclidean Manifold" if:

  • it is a closed connected smooth submanifold of $\mathbb R^n$,
  • for every $p, q$ in $M$, there is an Euclidean isometry $f$ sending $p$ to $q$ fixing $M$ (ie $f(M)=M$ and $f(p)=q$). The problem is to classify the "symmetric Euclidean Manifolds". I know there are several definitions of symmetric and homogeneous and that these spaces have been more or less classified so it may well be that my question is just a particular case. Thank you