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Post Closed as "Not suitable for this site" by abx, Johannes Hahn, Wolfgang, José Figueroa-O'Farrill, user1688
In question #2 I meant $M(3,\mathbb{R})!
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Mike Cocos
Mike Cocos
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For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done for other tensor bundles.

  1. Where can I find a good reference on this type of reductions?

  2. $PGL(2,\mathbb{R})$ acts by conjugation on the space of square matrices $M(2,\mathbb{R}).$$M(3,\mathbb{R}).$ Can one find any invariant polynomials associated to this action?

For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done for other tensor bundles.

  1. Where can I find a good reference on this type of reductions?

  2. $PGL(2,\mathbb{R})$ acts by conjugation on the space of square matrices $M(2,\mathbb{R}).$ Can one find any invariant polynomials associated to this action?

For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done for other tensor bundles.

  1. Where can I find a good reference on this type of reductions?

  2. $PGL(2,\mathbb{R})$ acts by conjugation on the space of square matrices $M(3,\mathbb{R}).$ Can one find any invariant polynomials associated to this action?

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Mike Cocos
Mike Cocos
  • 463
  • 3
  • 10

Tensor bundles as G structures

For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done for other tensor bundles.

  1. Where can I find a good reference on this type of reductions?

  2. $PGL(2,\mathbb{R})$ acts by conjugation on the space of square matrices $M(2,\mathbb{R}).$ Can one find any invariant polynomials associated to this action?