Projective Duality and Homogeneous Spaces


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Part A. Algebraic Steps.

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Part B. Constructing the homogeneous space.

Part C. An invariant metric on the homogenous space. The infinitesimal isotropy subalgebra at x consists of those infinitesimal generators which vanish at x.


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  6. Specifically we shall do the following:. Use the DifferrentialGeometry Library to define a 4 dimensional Lie algebra g. Construct the left and right invariant vector fields on G. Construct the Maurer Cartan forms on G.

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    Projective Geometry

    This is a comprehensive tutorial which illustrates a large number of commands from the DifferentialGeometry package and its subpackages. We first load in all the packages we shall need for this tutorial. Our goal is to construct a 3 dimensional homogeneous space for a 4-dimensional Lie group. We begin by looking at the 4 dimensional Lie algebras available for our use. All 4-dimensional Lie algebras have been classified and the results of these classifications are contained in the DifferentialGeometry Library.

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    References verbose ;. Academy of Sciences of Belarus, Ser.

    Duality, polarity and projective linear algebra - Differential Geometry 10 - NJ Wildberger

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      Projective Duality and Homogeneous Spaces Projective Duality and Homogeneous Spaces
      Projective Duality and Homogeneous Spaces Projective Duality and Homogeneous Spaces
      Projective Duality and Homogeneous Spaces Projective Duality and Homogeneous Spaces
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