Composing with the nearest point projection to Xg then, we have a quasi-isometric embedding of R3 into a product of Farey-graphs, which is impossible by [KL].
Coarse and synthetic Weil-Petersson geometry: quasi-flats, geodesics, and relative hyperbolicity
The action of Rn by translations in the y -coordinates is isometric and the projection M → U is a principal ﬁber bund le with structure group Rn .
Completeness in supergravity constructions
Corollary 2 Any complete projective special real manifold (H, gH ) of dimension n− 1 ≥ 0 admits a canonical realisation as a total ly geodesic submanifold of a complete projective special K¨ahler manifold (M , gM ) with a free isometric action of the group Rn .
Completeness in supergravity constructions
Theorem 5 The supergravity c-map maps any complete projective special K¨ahler domain (M , gM ) to a complete quaternionic K¨ahler manifold (N , gN ) of negative scalar curvature, which admits the free isometric action (3.4) of the group G.
Completeness in supergravity constructions
Corollary 3 Any complete projective special K¨ahler domain (M , gM ) admits a canonical realisation as a total ly geodesic K¨ahler submanifold of a complete quaternionic K¨ahler manifold (N , gN ) with a free isometric action of the group G.
Completeness in supergravity constructions
Let Φ : M → U ⊂ L be a smooth isometric immersion with respect to a Riemannian metric G on U and P : U → M a projection in the sense of Deﬁnition 3.12.
Area minimizers and boundary rigidity of almost hyperbolic metrics
Isometric square grid embeddings may be directly used as graph drawings, while planar projections of higher dimensional embeddings can be used to draw any partial cube , a class of graphs with many applications .
Isometric Diamond Subgraphs
Recall that a contractive linear pro jection P : X → Y is called an isometric reﬂection projection if I − 2P ∈ GX , or equivalently, if kI − 2P k = 1.
Convex-transitivity of Banach algebras via ideals
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