All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 109 Next

Displaying 2161 – 2180 of 5556

Showing per page

Isometric Embeddings of Pro-Euclidean Spaces

Barry Minemyer (2015)

Analysis and Geometry in Metric 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 immersions of the hyperbolic space H n ( - 1 ) into H n + 1 ( - 1 )

Ze-Jun Hu (1999)

Colloquium Mathematicae

We transform the problem of determining isometric immersions from H n ( - 1 ) into H n + 1 ( - 1 ) into that of solving equations of degenerate Monge-Ampère type on the unit ball B n ( 1 ) . 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.

Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups

Rory Biggs (2017)

Communications in Mathematics

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

Thomas Foertsch (2005)

Colloquium Mathematicae

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.

Isometries of systolic spaces

Tomasz Elsner (2009)

Fundamenta Mathematicae

We provide a classification of isometries of systolic complexes corresponding to the classification of isometries of CAT(0)-spaces. We prove that any isometry of a systolic complex either fixes the barycentre of some simplex (elliptic case) or stabilizes a thick geodesic (hyperbolic case). This leads to an alternative proof of the fact that finitely generated abelian subgroups of systolic groups are undistorted.

Currently displaying 2161 – 2180 of 5556