Manifold of Metrics with Fixed Volume Form
نویسندگان
چکیده
We study the manifold of all metrics with the fixed volume form on a compact Riemannian manifold of dimension ≥ 3. We compute the characteristic function for the L (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.
منابع مشابه
Einstein and Conformally Flat Critical Metrics of the Volume Functional
Let R be a constant. Let Mγ be the space of smooth metrics g on a given compact manifold Ω (n ≥ 3) with smooth boundary Σ such that g has constant scalar curvature R and g|Σ is a fixed metric γ on Σ. Let V (g) be the volume of g ∈ Mγ . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (·) in Mγ .
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