Hokkaido Mathematical Journal

Affine differential geometry of the unit normal vector fields of hypersurfaces in the real space forms

Kazuyuki HASEGAWA

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Abstract

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.

Article information

Source
Hokkaido Math. J., Volume 35, Number 3 (2006), 613-627.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766420

Digital Object Identifier
doi:10.14492/hokmj/1285766420

Mathematical Reviews number (MathSciNet)
MR2275505

Zentralblatt MATH identifier
1143.53011

Subjects
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]

Keywords
section of sphere bundle canonical metric metrically minimal affine immersion metrically totally umbilic affine immersion

Citation

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


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