Isometric embedding of the 2-sphere with non negative curvature in IR3.
Isometric Embeddings of Pro-Euclidean Spaces
In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...
Isometric Embeddings of Spherical spaceforms with cyclic fundamental groups.
Isometric equivalence of directions in Riemannian symmetric spaces.
Isometric immersions and induced geometric structures
In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.
Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations.
Isometric Immersions in Codimesion Two with Non Negative Curvature.
Isometric Immersions of Constant Curvature Manifolds.
Isometric immersions of domains of Lobachevski space in Euclidean spaces
Isometric immersions of Kähler manifolds
Isometric Immersions of Lorentzian Space Forms.
Isometric Immersions of n-dim. Hyperbolic Spaces into (4n?3)-dim. Standard Spheres and Hyperbolic Spaces.
Isometric immersions of Riemannian products revisited.
Isometric immersions of space forms and soliton theory.
Isometric Immersions of the Hyperbolic Plane into the Hyperbolic Space.
Isometric immersions of the hyperbolic space into
We transform the problem of determining isometric immersions from into into that of solving equations of degenerate Monge-Ampère type on the unit ball . By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
Isometric Immersions with the Same Gauss Map.
Isometric Reflections with Respect to Submanifolds and the Ricci Operator of Geodesic Spheres.
Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups
We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry is the...
Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces
We consider the Hausdorff metric on the space of compact convex subsets of a proper, geodesically complete metric space of globally non-positive Busemann curvature in which geodesics do not split, and characterize their surjective isometries. Moreover, an analogous characterization of the surjective isometries of the space of compact subsets of a proper, uniquely geodesic, geodesically complete metric space in which geodesics do not split is given.