Samiksha Jaiswal (Editor)

Rizza manifold

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In differential geometry a Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also referred as almost Hermitian Finsler manifold.

Formal definition

The content of this paragraph closely follows references (Rizza 1963) and (Ichijyō 1988), borrowing the scheme of notation equally from both sources. Precisely, given a differentiable manifold M and one of its points x ∈ M

  • TM is the tangent bundle of M;
  • TxM is the tangent space at x;

    • Definition 1. Let M be a 2n-dimensional Finsler manifold, n ≥ 1, and let F : TM → ℝ its Finsler function. If the condition

    (1)      F ( x , c y ) = | c | F ( x , y ) ∀ c ∈ C , x ∈ M , y ∈ T x M

    holds true, then M is a Rizza Manifold.

    References

    Rizza manifold Wikipedia
    (Text) CC BY-SA