Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Bang-yen Chen; Erhan Güler; Yusuf Yaylı; Hasan Hilmi Hacısalihoğlu

doi:10.36890/iejg.1216024

Review

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Year 2023, Volume: 16 Issue: 1, 4 - 47, 30.04.2023

Bang-yen Chen , Erhan Güler , Yusuf Yaylı , Hasan Hilmi Hacısalihoğlu

https://doi.org/10.36890/iejg.1216024

Cited By: 11

Abstract

The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation of submanifolds. Later, the first author and P. Piccinni extended the notion of finite type submanifolds to finite type maps of submanifolds; in particular, to submanifolds with finite type Gauss map. Since then, there have been rapid developments in the theory of finite type.
The simplest finite type submanifolds and submanifolds with finite type Gauss maps are those which are of 1-type. The classes of such submanifolds constitute very special and interesting families in the finite type theory.

Keywords

Finite type submanifold, Gauss map, spherical Gauss map, hyperbolic Gauss map, 1-type submanifold, self-intersection number

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Year 2023, Volume: 16 Issue: 1, 4 - 47, 30.04.2023

Bang-yen Chen , Erhan Güler , Yusuf Yaylı , Hasan Hilmi Hacısalihoğlu

https://doi.org/10.36890/iejg.1216024

Cited By: 11

Abstract

Keywords

Finite type submanifold, Gauss map, spherical Gauss ma, hyperbolic Gauss ma

References

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Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Article
Authors	Bang-yen Chen 0000-0002-1270-094X Erhan Güler 0000-0003-3264-6239 Yusuf Yaylı 0000-0003-4398-3855 Hasan Hilmi Hacısalihoğlu 0000-0002-1465-5986
Publication Date	April 30, 2023
Acceptance Date	February 19, 2023
Published in Issue	Year 2023 Volume: 16 Issue: 1

Cite

APA	Chen, B.-y., Güler, E., Yaylı, Y., Hacısalihoğlu, H. H. (2023). Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map. International Electronic Journal of Geometry, 16(1), 4-47. https://doi.org/10.36890/iejg.1216024
AMA	Chen By, Güler E, Yaylı Y, Hacısalihoğlu HH. Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map. Int. Electron. J. Geom. April 2023;16(1):4-47. doi:10.36890/iejg.1216024
Chicago	Chen, Bang-yen, Erhan Güler, Yusuf Yaylı, and Hasan Hilmi Hacısalihoğlu. “Differential Geometry of 1-Type Submanifolds and Submanifolds With 1-Type Gauss Map”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 4-47. https://doi.org/10.36890/iejg.1216024.
EndNote	Chen B-y, Güler E, Yaylı Y, Hacısalihoğlu HH (April 1, 2023) Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map. International Electronic Journal of Geometry 16 1 4–47.
IEEE	B.-y. Chen, E. Güler, Y. Yaylı, and H. H. Hacısalihoğlu, “Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 4–47, 2023, doi: 10.36890/iejg.1216024.
ISNAD	Chen, Bang-yen et al. “Differential Geometry of 1-Type Submanifolds and Submanifolds With 1-Type Gauss Map”. International Electronic Journal of Geometry 16/1 (April 2023), 4-47. https://doi.org/10.36890/iejg.1216024.
JAMA	Chen B-y, Güler E, Yaylı Y, Hacısalihoğlu HH. Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map. Int. Electron. J. Geom. 2023;16:4–47.
MLA	Chen, Bang-yen et al. “Differential Geometry of 1-Type Submanifolds and Submanifolds With 1-Type Gauss Map”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 4-47, doi:10.36890/iejg.1216024.
Vancouver	Chen B-y, Güler E, Yaylı Y, Hacısalihoğlu HH. Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map. Int. Electron. J. Geom. 2023;16(1):4-47.