Differential Geometry and Matrix-Based Generalizations of the Pythagorean Theorem in Space Forms

Differential Geometry and Matrix-Based Generalizations of the Pythagorean Theorem in Space Forms

In this work, we consider Pythagorean triples and quadruples using fundamental form matrices of hypersurfaces in three- and four-dimensional space forms and illustrate various figures. Moreover, we generalize that an immersed hypersphere <inline-formula><math xmlns="http://www.w3.org/1...

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Bibliographic Details
Main Authors: Erhan Güler, Yusuf Yaylı, Magdalena Toda
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
Subjects:
space forms
Pythagorean triples
Pythagorean quadruples
Pythagorean (<i>n</i> + 1)-tuples
hypersurface
hypersphere
Online Access:https://www.mdpi.com/2227-7390/13/5/836

Internet

https://www.mdpi.com/2227-7390/13/5/836

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