The space of totally real flat minimal surfaces in the Quaternionic projective space HP^3
Chuzi Duan, Ling He
TL;DR
This paper classifies the moduli space of certain totally real flat minimal surfaces in quaternionic projective space HP^3, revealing three 6-dimensional components and describing related minimal tori.
Contribution
It provides a complete description of the moduli space of noncongruent totally real flat minimal surfaces in HP^3, including their classification into three components.
Findings
Three moduli space components, each a 6-dimensional manifold.
Description of the moduli space of minimal tori in HP^3.
Classification of noncongruent totally real flat minimal immersions.
Abstract
We prove that the moduli space of all noncongruent linearly full totally real flat minimal immersions from the complex plane C into HP^3 that do not lie in CP^3 has three components, each of which is a manifold of real dimension 6. As an application, we give a description of the moduli space of all noncongruent linearly full totally real flat minimal tori in HP^3 that do not lie in CP^3.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Algebraic and Geometric Analysis · Geometric and Algebraic Topology