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replaced unrelated tags and deprecated tag 'geometry'; edited the question to make it clearer, I hope
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Ricardo Andrade
Ricardo Andrade
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Is the group of isometries of a homogeneous riemannianRiemannian manifold is maximal?

I have a homogenushomogeneous Riemannian manifold X with iaometryisometry group Iso. Is Iso a maximal group? By maximal group, I mean that there does not exist otheranother group G, such that:

  1. Iso is a proper subgroup of G,
  2. G act transitivlyacts transitively on X by difeomorphismsdiffeomorphisms, and
  3. G has compact stabilizers G_x,Gx.

I know, that if such a group exists, then there is a G-invariant metric on X. So, in other words, the question is: if I have a Riemannian metric d on X with isometry group Iso, which is homegenushomogeneous, could existscan there exist another Riemannian metric d' on X with isometry group Iso', such that Iso' contains properly the group Iso  ?

group of isometries homogeneous riemannian manifold is maximal

I have a homogenus Riemannian manifold X with iaometry group Iso. Is Iso a maximal group, I mean that does not exist other group G, such that:

  1. Iso is subgroup of G,
  2. G act transitivly on X by difeomorphisms,
  3. G has compact stabilizers G_x,

I know, that if such a group exists, then there is G-invariant metric on X. So in other words the question is: if I have Riemannian metric d on X with isometry group Iso, which is homegenus, could exists another Riemannian metric d' on X with isometry group Iso', such that Iso' contains properly group Iso  ?

Is the group of isometries of a homogeneous Riemannian manifold maximal?

I have a homogeneous Riemannian manifold X with isometry group Iso. Is Iso a maximal group? By maximal group, I mean that there does not exist another group G such that:

  1. Iso is a proper subgroup of G,
  2. G acts transitively on X by diffeomorphisms, and
  3. G has compact stabilizers Gx.

I know that if such a group exists, then there is a G-invariant metric on X. So, in other words, the question is: if I have a Riemannian metric d on X with isometry group Iso which is homogeneous, can there exist another Riemannian metric d' on X with isometry group Iso', such that Iso' contains properly the group Iso?

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Adam
Adam
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group of isometries homogeneous riemannian manifold is maximal

I have a homogenus Riemannian manifold X with iaometry group Iso. Is Iso a maximal group, I mean that does not exist other group G, such that:

  1. Iso is subgroup of G,
  2. G act transitivly on X by difeomorphisms,
  3. G has compact stabilizers G_x,

I know, that if such a group exists, then there is G-invariant metric on X. So in other words the question is: if I have Riemannian metric d on X with isometry group Iso, which is homegenus, could exists another Riemannian metric d' on X with isometry group Iso', such that Iso' contains properly group Iso ?