Title

Gauss maps and duality of sphere bundles

Document Type

Article

Publication Date

1-1-2016

Subject Area

ARRAY(0x5575b06ebdd0)

Abstract

Given a sphere bundle, we define a Gauss map of the bundle, and from this we define an orthogonal sphere bundle. We define the dual of a Gauss map, and show that it is equal to either the orthogonal bundle or the singularity set of the orthogonal bundle’s Gauss map. This is a direct generalization of the case where the bundles are the unit tangent and unit normal bundles of an immersed manifold. The theory is supported by several examples. We end with looking at the duals of certain submanifolds of the sphere bundle.

Publication Title

Contemporary Mathematics

Volume

675

First Page

77

Last Page

88

Digital Object Identifier (DOI)

10.1090/conm/675/13584

ISSN

02714132

E-ISSN

10983627

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