Adrian Constantin, Boris Kolev
Abstract
Each Hk inner product, k ∈ N, endows the diffeomorphism group of the circle with a Riemannian structure. For k ≥ 1 the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of geodesics holds. 1
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Each Hk inner product, k ∈ N, endows the diffeomorphism group of the circle with a Riemannian structure. For k ≥ 1 the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of geodesics holds. 1
Key concepts: Diffeomorphism, Mathematics, Exponential map (Riemannian geometry), Geodesic, Group (periodic table), Pure mathematics, Product (mathematics), Property (philosophy)