Bulletin of the Belgian Mathematical Society - Simon Stevin

Associated Families of Surfaces in Warped Products and Homogeneous Spaces

Marie-Amélie Lawn and Miguel Ortega

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Abstract

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely, rotating structure vector field). We prove that, provided the surface is not totally umbilical, such families exist in both cases if, and only if, the ambient manifold is a product and the surface is minimal. In particular, there exists no associated families of surfaces with rotating structure vector field in the Heisenberg group.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 3 (2019), 321-339.

Dates
First available in Project Euclid: 17 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1568685650

Digital Object Identifier
doi:10.36045/bbms/1568685650

Mathematical Reviews number (MathSciNet)
MR4007601

Subjects
Primary: 53B25: Local submanifolds [See also 53C40] 53B20: Local Riemannian geometry 53B30: Lorentz metrics, indefinite metrics

Keywords
Associated families of surfaces 3-dim spaces (semi-Riemannian) warped products homogenous spaces immersions

Citation

Lawn, Marie-Amélie; Ortega, Miguel. Associated Families of Surfaces in Warped Products and Homogeneous Spaces. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 3, 321--339. doi:10.36045/bbms/1568685650. https://projecteuclid.org/euclid.bbms/1568685650


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