Spherical 2-Dupin submanifolds
Antonio J. Di Scala, Guilherme Machado de Freitas
TL;DR
This paper classifies certain special submanifolds in space forms, showing that non-hyperspherical spherical 2-Dupin submanifolds are conformally equivalent to classical projective planes, and also classifies related submanifolds.
Contribution
It provides a complete classification of spherical 2-Dupin submanifolds not being hypersurfaces and characterizes 2-CPC, 2-umbilical, and weakly 2-umbilical submanifolds in space forms.
Findings
Non-hyperspherical spherical 2-Dupin submanifolds are conformally congruent to classical projective planes.
Classification of 2-CPC, 2-umbilical, and weakly 2-umbilical submanifolds.
Identification of conformal congruences with standard embeddings.
Abstract
We show that every spherical 2-Dupin submanifold that is not a hypersurface is conformally congruent to the standard embedding of the real, complex, quaternionic or octonionic projective plane. We also classify 2-CPC, 2-umbilical and weakly 2-umbilical submanifolds in space forms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology