Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 35, Number 3 (2006), 613-627.
Affine differential geometry of the unit normal vector fields of hypersurfaces in the real space forms
In this paper, for a hypersurface in the real space form of constant curvature, we prove that the unit normal vector field is an affine imbedding into a certain sphere bundle with canonical metric. Moreover, we study the relations between a hypersurface and its unit normal vector field as an affine imbedding. In particular, several hypersurfaces are characterized by affine geometric conditions which are independent of the choice of the transversal bundle.
Hokkaido Math. J., Volume 35, Number 3 (2006), 613-627.
First available in Project Euclid: 29 September 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
HASEGAWA, Kazuyuki. Affine differential geometry of the unit normal vector fields of hypersurfaces in the real space forms. Hokkaido Math. J. 35 (2006), no. 3, 613--627. doi:10.14492/hokmj/1285766420. https://projecteuclid.org/euclid.hokmj/1285766420