120 research outputs found
ADDENDUM TO: MAXIMAL TORI OF EXTRINSIC SYMMETRIC SPACES AND MERIDIANS
Improving a theorem in [1] we observe that a maximal torus of an extrinsic symmetric space in a euclidean space V is itself extrinsic symmetric in some affine subspace of V
Compatibility of Gauss maps with metrics
We give necessary and sufficient conditions on a smooth local map of a
Riemannian manifold into the sphere to be the Gauss map of an
isometric immersion , . We briefly discuss the case of
general as wellComment: 14 pages, no figure
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 of rank divisible
by four over a finite complex we derive a stable decomposition result for
vector bundles over the sphere bundle in terms of vector bundles and Clifford module bundles over . After
passing to topological K-theory these results imply classical Bott-Thom
isomorphism theorems.Comment: 37 pages, 13 figures; minor edits; published versio
Geometrie – Anschauung und Begriffe: Vorstellen, Verstehen, Weiterdenken: eine Einführung für Studierende
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