Higher codimensional Euclidean helix submanifolds

Kodai Mathematical Journal

Antonio J. Di Scala¹  Gabriel Ruiz-Hernández² 

[1] Dipartimento di Matematica Politecnico di Torino;Mathematics Department Massachusetts Institute of Technology

关键词: helix submanifold;    constant angle submanifolds;    eikonal equation;   

DOI  :  10.2996/kmj/1278076336

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(14)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.

【 授权许可】

Unknown