Pythagorean Submanifolds in Euclidean Spaces

被引：0

作者：

Aydin, Muhittin Evren ^{[1
]}

Mihai, Adela ^{[2
,3
]}

Ozgur, Cihan ^{[4
]}

机构：

[1] Firat Univ, Fac Sci, Dept Math, TR-23200 Elazig, Turkiye

[2] Tech Univ Civil Engn Bucharest, Dept Math & Comp Sci, Bucharest 020396, Romania

[3] Transilvania Univ Brasov, Interdisciplinary Doctoral Sch, Brasov 500036, Romania

[4] Izmir Democracy Univ, Dept Math, TR-35140 Izmir, Turkiye

来源：

RESULTS IN MATHEMATICS | 2023年 / 78卷 / 06期

关键词：

Matrix Pythagorean triple; golden ratio; shape operator; Clifford torus; isoparametric submanifold; METALLIC SHAPED HYPERSURFACES;

D O I：

10.1007/s00025-023-01985-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce the notion of a Pythagorean sub manifold isometrically immersed into a Euclidean space. This definiton will be based on the shape operator of the submanifold. We prove that any Pythagorean submanifold in a Euclidean space is isoparametric, the principal curvatures along any parallel normal vector field being given in terms of the golden or conjugate golden ratios. In addition, we obtain that a Pythagorean submanifold of codimension 1 (resp. = 2) is totally umbilical (resp. pseudo-umbilical), classifying those submanifolds.

引用

页数：15

共 19 条

[1] Abe N., 1987, Yokohama Math. J, V35, P123
[2] Alvarez-Vizoso J, 2022, Arxiv, DOI arXiv:2209.06246
[3] On Matrix Pythagorean Triples
Arnold, Maxim
Eydelzon, Anatoly
[J]. AMERICAN MATHEMATICAL MONTHLY, 2019, 126 (02) : 158 - 160
[4] Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms
Aydin, Muhittin Evren
Mihai, Adela
Ozgur, Cihan
[J]. AXIOMS, 2022, 11 (02)
[5] A Note on Surfaces in Space Forms with Pythagorean Fundamental Forms
Aydin, Muhittin Evren
Mihai, Adela
[J]. MATHEMATICS, 2020, 8 (03)
[6] THERE IS MORE THAN ONE WAY TO FRAME A CURVE
BISHOP, RL
[J]. AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (03) : 246 - 251
[7] Isoparametric and Dupin Hypersurfaces
Cecil, Thomas E.
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2008, 4
[8] Chen B.Y., 2015, Total Mean Curvature and Submanifolds of Finite Type, V2nd ed.
[9] SURFACE WITH PARALLEL MEAN CURVATURE VECTOR
CHEN, BY
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1973, 22 (07) : 655 - 666
[10] GOLDEN- AND PRODUCT-SHAPED HYPERSURFACES IN REAL SPACE FORMS
Crasmareanu, Mircea
Hretcanu, Cristina-Elena
Munteanu, Marian-Ioan
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2013, 10 (04)

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