Abstract
In this paper, we study a particular class of submanifolds, which we call Pythagorean submanifolds, in one of the standard complete simply connected models of real space forms. They are defined by an equation based on the shape operator. We give several examples and observe that any Pythagorean submanifold is isoparametric where the principal curvatures are given in terms of the Golden ratio. We also classify Pythagorean hypersurfaces.
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Aydın, M.E., Mihai, A., Özgür, C. (2024). Pythagorean Submanifolds. In: Chen, BY., Choudhary, M.A., Khan, M.N.I. (eds) Geometry of Submanifolds and Applications. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-99-9750-3_4
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DOI: https://doi.org/10.1007/978-981-99-9750-3_4
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