| Title:
|
A Wintgen type inequality and characterization of hyperbolic points on surfaces sitting in the Euclidean four-space (English) |
| Author:
|
Khajeh Salehani, Mahdi |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2026 |
| Pages:
|
43-67 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to explore the relations between some geometric invariants associated with surfaces immersed in the Euclidean four-space, by investigating the extrinsic and intrinsic geometries of our surfaces from a global point of view, as well as considering the curvature ellipses of a given surface and their associated isoptic curves. We establish an elegant formula which shows how the isoptic curves of the curvature ellipses of a given surface are related to the asymptotic directions on the surface, and derive a Wintgen type inequality which provides both a simple relationship between the main intrinsic and extrinsic invariants, and a natural and geometric characterization of the hyperbolic points, on the given surface. To indicate an application of our Wintgen type inequality to the theory of M$\ddot{\mbox {o}}$bius invariant Euclidean submanifolds, we conclude the paper with a novel geometric result on a remarkable family of surfaces known as Wintgen ideal surfaces. (English) |
| Keyword:
|
normal curvature |
| Keyword:
|
mean curvature |
| Keyword:
|
asymptotic field |
| Keyword:
|
hyperbolic point |
| Keyword:
|
isoptic curve |
| Keyword:
|
Wintgen ideal surface |
| MSC:
|
53C05 |
| MSC:
|
53C40 |
| MSC:
|
53C42 |
| DOI:
|
10.5817/AM2026-2-43 |
| . |
| Date available:
|
2026-06-03T08:15:58Z |
| Last updated:
|
2026-06-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153665 |
| . |
| Reference:
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