Higher codimensional Euclidean helix submanifolds

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概要

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• A submanifold of Rn whose tangent space makes constant angle with a fixed direction d is called a helix. Helix submanifolds are related with the eikonal PDE equation. We give a method to find every solution to the eikonal PDE on a Riemannian manifold locally. As a consequence we give a local construction of arbitrary Euclidean helix submanifolds of any dimension and codimension. Also we characterize the ruled helix submanifolds and in particular we describe those which are minimal.

• 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文

著者

• Di Scala

  Dipartimento Di Matematica Politecnico Di Torino

• Ruiz-Hernández Gabriel

  Mathematics Department Massachusetts Institute of Technology

関連論文

• Parallel Kahler submanifolds of quaternionic Kahler symmetric spaces
• Higher codimensional Euclidean helix submanifolds

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