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Codazzi and totally umbilical hypersurfaces in $\mathrm {Sol}_1^4$

Part of: Global differential geometry

Published online by Cambridge University Press:  03 April 2025

Zlatko Erjavec Open the ORCID record for Zlatko Erjavec [Opens in a new window]  and
Jun-ichi Inoguchi Open the ORCID record for Jun-ichi Inoguchi [Opens in a new window]
Zlatko Erjavec*
Affiliation:
Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia
Jun-ichi Inoguchi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, Japan
*
Corresponding author: Zlatko Erjavec; Email: [email protected]
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Abstract

In this paper, we prove the non-existence of Codazzi and totally umbilical hypersurfaces, especially totally geodesic hypersurfaces, in the $4$-dimensional model space $\mathrm {Sol}_1^4$.

Keywords

Codazzi hypersurfaceparallel hypersurfacetotally umbilicaltotally geodesicsolvable Lie group

MSC classification

Primary: 53C30: Homogeneous manifolds
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C40: Global submanifolds
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 7
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

†

The authors dedicate this article to Professor Toshiyuki Akita on the occasion of his 60th birthday.

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