Geometry & Topology
- Geom. Topol.
- Volume 15, Number 2 (2011), 699-705.
Directed immersions of closed manifolds
Given any finite subset of the sphere , , which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space whose Gauss map misses . In particular, this answers a question of M Gromov.
Geom. Topol., Volume 15, Number 2 (2011), 699-705.
Received: 25 October 2010
Accepted: 13 March 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 57R42: Immersions 58K15: Topological properties of mappings
Ghomi, Mohammad. Directed immersions of closed manifolds. Geom. Topol. 15 (2011), no. 2, 699--705. doi:10.2140/gt.2011.15.699. https://projecteuclid.org/euclid.gt/1513732302