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Minimal Submanifolds in \({{\textrm{Sol}}}_0^4\)

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Abstract

Minimal invariant, minimal totally real, and minimal CR-submanifolds in the 4-dimensional homogeneous solvable Lie group \({{\textrm{Sol}}}_0^4\) equipped with standard globally conformal Kähler structure are studied.

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Acknowledgements

The authors would like to thank professor Shimpei Kobayashi for his suggestions to the proof of Theorem 5.11. We would also like to thank the anonymous reviewer for careful reading of our manuscript and for the constructive comments and suggestions for improvement of this paper. In particular, the reviewer suggested the authors to mention the relations of the present work and the recent work [10] which has done after the first version of this manuscript was completed. Moreover,Problem 6.4 is motivated by reviewer’s comment.

Funding

The second author is partially supported by JSPS KAKENHI Grant Numbers JP15K04834, JP19K03461, JP23K03081.

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Author notes

  1. Zlatko Erjavec and Jun-ichi Inoguchi have contributed equally to this work.

Authors and Affiliations

  1. University of Zagreb, Faculty of Organization and Informatics, HR-42000, Varaždin, Pavlinska 2, Croatia

    Zlatko Erjavec

  2. University of Tsukuba, Institute of Mathematics, 305-8571, Tsukuba, 1-1-1 Tennodai, Japan

    Jun-ichi Inoguchi

  3. Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan

    Jun-ichi Inoguchi

Authors
  1. Zlatko Erjavec
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  2. Jun-ichi Inoguchi
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Correspondence to Zlatko Erjavec.

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Erjavec, Z., Inoguchi, Ji. Minimal Submanifolds in \({{\textrm{Sol}}}_0^4\). J Geom Anal 33, 274 (2023). https://doi.org/10.1007/s12220-023-01323-9

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