No Access

Real hypersurfaces with isometric Reeb flow in Kähler manifolds

Jürgen Berndt

Department of Mathematics, King’s College London, London WC2R 2LS, UK

E-mail Address: jurgen.berndt@kcl.ac.uk

Search for more papers by this author

and

Young Jin Suh

Department of Mathematics and RIRCM, Kyungpook National University, Daegu 41566, Republic of Korea

E-mail Address: yjsuh@knu.ac.kr

Search for more papers by this author

https://doi.org/10.1142/S0219199719500391Cited by:7 (Source: Crossref)

Abstract

We investigate the structure of real hypersurfaces with isometric Reeb flow in Kähler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian symmetric spaces of compact type.

Keywords:

AMSC: 53C40, 32M15, 37C10, 53C55, 53D15

References

1. J. F. Adams, Lectures on Exceptional Lie Groups, Chicago Lectures in Mathematics (University of Chicago Press, Chicago, IL, 1996). Google Scholar
2. W. Ballmann, Lectures on Kähler Manifolds, ESI Lectures in Mathematics and Physics (European Mathematical Society (EMS), Zürich, 2006). Crossref, Google Scholar
3. J. Berndt, S. Console and C. E. Olmos, Submanifolds and Holonomy, 2nd edn., Monographs and Research Notes in Mathematics (CRC Press, Boca Raton, FL, 2016). Crossref, Google Scholar
4. J. Berndt and C. Olmos, Maximal totally geodesic submanifolds and index of symmetric spaces, J. Differential Geom. 104(2) (2016) 187–217. Crossref, Web of Science, Google Scholar
5. J. Berndt and C. Olmos, On the index of symmetric spaces, J. Reine Angew. Math. 737 (2018) 33–48. Crossref, Web of Science, Google Scholar
6. J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb flow in complex quadrics, Internat. J. Math. 24(7) (2013) 1350050, 18 pp. Link, Web of Science, Google Scholar
7. J. Berndt and L. Vanhecke, Curvature-adapted submanifolds, Nihonkai Math. J. 3(2) (1992) 177–185. Google Scholar
8. A. Borel and J. De Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949) 200–221. Crossref, Google Scholar
9. B. Y. Chen and T. Nagano, Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45(2) (1978) 405–425. Crossref, Web of Science, Google Scholar
10. A. Gray, Tubes, 2nd edn., Progress in Mathematics, Vol. 221 (Birkhäuser Verlag, Basel, 2004). Crossref, Google Scholar
11. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Mathematics, Vol. 34 (American Mathematical Society, Providence, RI, 2001). Crossref, Google Scholar
12. S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20(2) (1986) 245–261. Crossref, Web of Science, Google Scholar
13. M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975) 355–364. Crossref, Web of Science, Google Scholar
14. A. L. Onishchik, O vpolne geodezicheskih podmnogoobraziyah simmetricheskih prostranstv, Geometricheskie metody v zadachah analiza i algebry 2 (1980) 64–85. Google Scholar
15. H. Samelson, Notes on Lie Algebras, 2nd edn., Universitext (Springer-Verlag, New York, 1990). Crossref, Google Scholar
16. Y. J. Suh, Real hypersurfaces in the complex hyperbolic quadric with isometric Reeb flow, Commun. Contemp. Math. 20(2) (2018) 1750031, 20 pp. Link, Web of Science, Google Scholar