arXiv subjects

Jost-Hinrich Eschenburg

Publications and source records attributed to Jost-Hinrich Eschenburg.

4 recordsLinked to original sources

arXiv2025

Symmetric Spaces with Rectangular Unit Lattices, Revisited

We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way.

math.DG↗

arXiv2025

Extrinsically Symmetric Spaces, Submanifolds of Clifford Type and a Theorem of Harish-Chandra

We prove that a compact, intrinsically symmetric submanifold of a Euclidean space is extrinsically symmetric if and only if its maximal tori are Clifford tori in the ambient space. Moreover, we show that this result can be used to give a geometric proof of a result of Harish-Chandra on strongly orthogonal roots in semisimple Lie algebras.

math.DG↗

arXiv2021

Bott-Thom isomorphism, Hopf bundles and Morse theory

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable range, to mapping spaces associated to orthogonal Clifford representations. Given an oriented Euclidean bundle $V \to X$ of rank divisible by four over a finite complex $X$ we derive a stable decomposition result for vector bundles over the sphere bundle $\mathord{\mathbb S}( \mathbb{R} \oplus V)$ in terms of vector bundles and Clifford module bundles over $X$. After passing to topological K-theory these results imply classical Bott-Thom isomorphism theorems.

math.AT↗

arXiv2007

Almost positive curvature on the Gromoll-Meyer sphere

Gromoll and Meyer have represented a certain exotic 7-sphere $Σ^7$ as a biquotient of the Lie group $G = Sp(2)$. We show for a 2-parameter family of left invariant metrics on $G$ that the induced metric on $Σ^7$ has strictly positive sectional curvature at all points outside four subvarieties of codimension $\geq 1$ which we describe explicitly.

math.DG↗