Illinois Journal of Mathematics

Helix, shadow boundary and minimal submanifolds

Gabriel Ruiz-Hernández

Full-text: Open access

Abstract

We give conditions for the shadow boundary of a Riemannian submanifold $M$ to be regular. We prove that a helix hypersurface is ruled. By studying some relations between these natural submanifolds, we show that a minimal helix shadow boundary hypersurface of $M$ is totally geodesic in $M$.

Article information

Source
Illinois J. Math., Volume 52, Number 4 (2008), 1385-1397.

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258554368

Digital Object Identifier
doi:10.1215/ijm/1258554368

Mathematical Reviews number (MathSciNet)
MR2595773

Zentralblatt MATH identifier
1181.53047

Subjects
Primary: 53C40: Global submanifolds [See also 53B25] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Ruiz-Hernández, Gabriel. Helix, shadow boundary and minimal submanifolds. Illinois J. Math. 52 (2008), no. 4, 1385--1397. doi:10.1215/ijm/1258554368. https://projecteuclid.org/euclid.ijm/1258554368


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