Taiwanese Journal of Mathematics

Minimal Ruled Submanifolds Associated with Gauss Map

Sun Mi Jung, Dong-Soo Kim, and Young Ho Kim

Full-text: Open access

Abstract

We set up the new models of product manifolds, namely a generalized circular cylinder and a generalized hyperbolic cylinder as cylindrical types of ruled submanifold in Minkowski space. We also establish some characterizations of generalized circular cylinders and hyperbolic cylinders in Minkowski space with the Gauss map. We also show that there do not exist non-cylindrical marginally trapped ruled submanifolds with the pointwise $1$-type Gauss map of the first kind, which gives a characterization of non-cylindrical minimal ruled submanifolds in Minkowski space.

Article information

Source
Taiwanese J. Math., Volume 22, Number 3 (2018), 567-605.

Dates
Received: 7 March 2017
Revised: 18 September 2017
Accepted: 30 September 2017
First available in Project Euclid: 26 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1508983231

Digital Object Identifier
doi:10.11650/tjm/170908

Mathematical Reviews number (MathSciNet)
MR3807326

Zentralblatt MATH identifier
06965386

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

Keywords
generalized circular cylinder generalized hyperbolic cylinder marginally trapped ruled submanifold minimal ruled submanifold

Citation

Jung, Sun Mi; Kim, Dong-Soo; Kim, Young Ho. Minimal Ruled Submanifolds Associated with Gauss Map. Taiwanese J. Math. 22 (2018), no. 3, 567--605. doi:10.11650/tjm/170908. https://projecteuclid.org/euclid.twjm/1508983231


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