Publications of Jürgen Berndt


BOOKS
  1. Generalized Heisenberg groups and Damek-Ricci harmonic spaces (with Franco Tricerri and Lieven Vanhecke), Lecture Notes in Mathematics 1598, Springer-Verlag, Berlin, 1995, viii+125 pp. ISBN: 3-540-59001-3.
  2. Submanifolds and holonomy (with Sergio Console and Carlos Olmos), Chapman & Hall/CRC Research Notes in Mathematics 434, Chapman & Hall/CRC, Boca Raton, FL, 2003, x+336 pp. ISBN: 1-58488-371-5.
  3. Submanifolds and holonomy, second edition (with Sergio Console and Carlos Olmos), Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2016, xxxviii+456 pp. ISBN: 978-1-4822-4515-8.
  4. Real hypersurfaces in Hermitian symmetric spaces (with Young Jin Suh), Advances in Analysis and Geometry, Walter De Gruyter GmbH, Berlin/Boston, 2022. ISBN 978-3-11-068978-5

RESEARCH ARTICLES
  1. Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132-141.
  2. Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math. 419 (1991), 9-26.
  3. Geodesic sprays and C- and P-spaces (with Lieven Vanhecke). Differential Geometry (Turin, 1992). Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), no. 4, 343-358 (1993).
  4. Curvature-adapted submanifolds (with Lieven Vanhecke), Nihonkai Math. J. 3 (1992), no. 2, 177-185.
  5. Two natural generalizations of locally symmetric spaces (with Lieven Vanhecke), Differential Geom. Appl. 2 (1992), no. 1, 57-80.
  6. Three-dimensional Einstein-like manifolds, Differential Geom. Appl. 2 (1992), no. 4, 385-397.
  7. Naturally reductive Riemannian homogeneous spaces and real hypersurfaces in complex and quaternionic space forms (with Lieven Vanhecke). Differential geometry and its applications (Opava, 1992), 353-364, Math. Publ., 1, Silesian Univ. Opava, Opava, 1993. pdf
  8. Geodesic spheres and generalizations of locally symmetric spaces (with Lieven Vanhecke), Boll. Un. Mat. Ital. A (7) 7 (1993), no. 1, 125-134.
  9. Minimal Liouville surfaces in Euclidean spaces (with John Bolton and Lyndon Woodward). Geometry and topology of submanifolds, V (Leuven/Brussels, 1992), 26-40, World Sci. Publ., River Edge, NJ, 1993. pdf
  10. Geometry of generalized Heisenberg groups and their Damek-Ricci harmonic extensions (with Franco Tricerri and Lieven Vanhecke), C. R. Math. Acad. Sci. Paris Sér I Math. 318 (1994), no. 5, 471-476.
  11. Symmetric-like Riemannian manifolds and geodesic symmetries (with Friedbert Prüfer and Lieven Vanhecke), Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), no. 2, 265-282.
  12. Almost complex curves and hypersurfaces in the nearly Kähler 6-sphere (with John Bolton and Lyndon Woodward), Geom. Dedicata 56 (1995), no. 3, 237-247.
  13. Geometry of weakly symmetric spaces (with Lieven Vanhecke), J. Math. Soc. Japan 48 (1996), no. 4, 745-760.
  14. Geodesic spheres and two-point homogeneous spaces (with Friedbert Prüfer and Lieven Vanhecke), Israel J. Math. 93 (1996), 373-385.
  15. Examples of weakly symmetric spaces in contact geometry (with Philippe Tondeur and Lieven Vanhecke), Boll. Un. Mat. Ital. B (7) 11 (1997), no. 2, suppl., 1-10.
  16. Geodesics in weakly symmetric spaces (with Oldrich Kowalski and Lieven Vanhecke), Ann. Global Anal. Geom. 15 (1997), no. 2, 153-156.
  17. Riemannian geometry of complex two-plane Grassmannians, Rend. Sem. Mat. Univ. Politec. Torino 55 (1997), no. 1, 19-83.
  18. Weakly symmetric groups of Heisenberg type (with Fulvio Ricci and Lieven Vanhecke), Differential Geom. Appl. 8 (1998), no. 3, 275-284.
  19. Totally geodesic submanifolds of symmetric-like Riemannian manifolds (with Friedbert Prüfer and Lieven Vanhecke), Tsukuba J. Math. 22 (1998), no. 2, 463-475. (Erratum)
  20. Homogeneous hypersurfaces in hyperbolic spaces, Math. Z. 229 (1998), no. 4, 589-600.
  21. φ-symmetric spaces and weak symmetry (with Lieven Vanhecke), Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 2 (1999), no. 2, 389-392.
  22. Real hypersurfaces in complex two-plane Grassmannians (with Young Jin Suh), Monatsh. Math. 127 (1999), no. 1, 1-14.
  23. On infinitesimally k-flat homogeneous spaces (with Evangelia Samiou), Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 1, 61-66.
  24. On index number and topology of flag manifolds (with Sergio Console and Anna Fino), Differential Geom. Appl. 15 (2001), no. 1, 81-90.
  25. Cohomogeneity one actions on hyperbolic spaces (with Martina Brück), J. Reine Angew. Math. 541 (2001), 209-235.
  26. Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians (with Young Jin Suh), Monatsh. Math. 137 (2002), no. 2, 87-98.
  27. Rank rigidity, cones, and curvature-homogeneous Hadamard manifolds (with Evangelia Samiou), Osaka J. Math. 39 (2002), no. 2, 383-394.
  28. Harmonic and minimal unit vector fields on Riemannian symmetric spaces (with Lieven Vanhecke and Laszlo Verhoczki), Illinois J. Math. 47 (2003), no. 4, 1273-1286.
  29. Homogeneous codimension one foliations on noncompact symmetric spaces (with Hiroshi Tamaru), J. Differential Geom. 63 (2003), no. 1, 1-40.
  30. Geodesics on the unit tangent bundle (with Eric Boeckx, Peter Nagy and Lieven Vanhecke), Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 6, 1209-1229.
  31. Projective planes, Severi varieties and spheres (with Michael Atiyah). Surveys in differential geometry, Vol. VIII (Boston, MA, 2002), 1027, Surv. Differ. Geom., 8, Int. Press, Somerville, MA, 2003.
  32. Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit (with Hiroshi Tamaru), Tohoku Math. J. (2) 56 (2004), no. 2, 163-177.
  33. Symmetric submanifolds associated with irreducible symmetric R-spaces (with Jost-Hinrich Eschenburg, Hiroo Naitoh and Kazumi Tsukada), Math. Ann. 332 (2005), no. 4, 721-737.
  34. Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces (with José Carlos Díaz-Ramos), J. London Math. Soc. (2) 74 (2006), no. 3, 778-798.
  35. Cohomogeneity one actions on noncompact symmetric spaces of rank one (with Hiroshi Tamaru), Trans. Amer. Math. Soc. 359 (2007), no. 7, 3425-3438.
  36. Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane (with José Carlos Díaz-Ramos), Proc. Amer. Math. Soc. 135 (2007), no. 10, 3349-3357.
  37. Homogeneous hypersurfaces in complex hyperbolic spaces (with José Carlos Díaz-Ramos), Geom. Dedicata 138 (2009), 129-150.
  38. Hyperpolar homogeneous foliations on symmetric spaces of noncompact type (with José Carlos Díaz-Ramos and Hiroshi Tamaru), J. Differential Geom. 86 (2010), no. 2, 191-235.
  39. Homogeneous polar foliations of complex hyperbolic spaces (with José Carlos Díaz-Ramos), Comm. Anal. Geom. 20 (2012), no. 3, 435-454.
  40. Hypersurfaces in noncompact complex Grassmannians of rank two (with Young Jin Suh), Internat. J. Math. 23 (2012), no. 10, 1250103, 35 pp.
  41. On the geometry of homogeneous real hypersurfaces in the complex quadric (with Young Jin Suh). Proceedings of the 16th International Workshop on Differential Geometry and the 5th KNUGRG-OCAMI Differential Geometry Workshop, 1-9, Natl. Inst. Math. Sci. (NIMS), Taejon, 2012. pdf
  42. Polar actions on the complex hyperbolic plane (with José Carlos Díaz-Ramos), Ann. Global Anal. Geom. 43 (2013), no. 1, 99-106.
  43. Real hypersurfaces with isometric Reeb flow in complex quadrics (with Young Jin Suh), Internat. J. Math. 24 (2013), no. 7, 1350050, 18 pp.
  44. Cohomogeneity one actions on symmetric spaces of noncompact type (with Hiroshi Tamaru), J. Reine Angew. Math. 683 (2013), 129-159.
  45. Contact hypersurfaces in noncompact complex Grassmannians of rank two (with Hyunjin Lee and Young Jin Suh), Internat. J. Math. 24 (2013), 1350089, 11 pp.
  46. Contact hypersurfaces in Kähler manifolds (with Young Jin Suh), Proc. Amer. Math. Soc 143 (2015), no. 6, 2637-2649.
  47. Cohomogeneity one actions on some noncompact symmetric spaces of rank two (with Miguel Domínguez-Vázquez), Transform. Groups 20 (2015), no. 4, 921-938.
  48. Maximal totally geodesic submanifolds and index of symmetric spaces (with Carlos Olmos), J. Differential Geom. 104 (2016), no. 2, 187-217.
  49. Compact homogeneous Riemannian manifolds with low co-index of symmetry (with Carlos Olmos and Silvio Reggiani), J. Eur. Math. Soc. (JEMS) 19 (2017), no. 1, 221-254.
  50. Cohomogeneity one actions on Minkowski spaces (with José Carlos Díaz-Ramos and Mohammad Javad Vanaei), Monatsh. Math. 184 (2017), no. 2, 185-200.
  51. The index of compact simple Lie groups (with Carlos Olmos), Bull. Lond. Math. Soc. 49 (2017), no. 5, 903-907.
  52. On the index of symmetric spaces (with Carlos Olmos), J. Reine Angew. Math. 737 (2018), 33-48.
  53. Real hypersurfaces with isometric Reeb flow in Kähler manifolds (with Young Jin Suh), Commun. Contemp. Math. 23 (2021), no. 1, Paper No. 1950039, 33 pp.
  54. The index conjecture for symmetric spaces (with Carlos Olmos), J. Reine Angew. Math. 772 (2021), 187-222.
  55. The index of exceptional symmetric spaces (with Carlos Olmos and Juan Sebastián Rodríguez), Rev. Mat. Iberoam. 37 (2021), no. 4, 1599-1627.
  56. Foliated Hopf hypersurfaces in complex hyperbolic quadrics, Ann. Mat. Pura Appl. (4) 202 (2023), no. 2, 619-655.
  57. Submanifolds with constant principal curvatures in Riemannian symmetric spaces (with Víctor Sanmartín-López), to appear in Comm. Anal. Geom. Preprint arXiv:1805.10088 [math.DG].

SURVEY ARTICLES
  1. Real hypersurfaces with constant principal curvatures in complex space forms. Geometry and topology of submanifolds, II (Avignon, 1988), 10-19, World Sci. Publ., Teaneck, NJ, 1990. pdf
  2. Aspects of the geometry of the Jacobi operator (with Lieven Vanhecke). Differential geometry, complex analysis (Parma, 1994). Riv. Mat. Univ. Parma (5) 3 (1994), no. 1, 91-108 (1995).
  3. On curvature and submanifolds of complex two-plane Grassmannians. Proceedings of the Second International Workshop on Differential Geometry (Taegu, 1997), 1-15, Kyungpook Natl. Univ., Taegu, 1998. pdf
  4. On homogeneous hypersurfaces in Riemannian symmetric spaces. Proceedings of the Second International Workshop on Differential Geometry (Taegu, 1997), 17-34, Kyungpook Natl. Univ., Taegu, 1998. pdf
  5. Geometry of weakly symmetric spaces. Proceedings of the Fourth International Workshop on Differential Geometry and Its Applications, (Brasov, 1999), 66-73, Transilvania Univ. Press, Brasov, 2000. pdf
  6. Symmetric submanifolds of symmetric spaces. Proceedings of the Seventh International Workshop on Differential Geometry (KMS Special Session on Geometry) (Taegu, 2002), 1-15, Kyungpook Natl. Univ., Taegu, 2003. pdf
  7. Real hypersurfaces with constant principal curvatures in complex space forms. Proceedings of the Tenth International Workshop on Differential Geometry, 1-12, Kyungpook Natl. Univ., Taegu, 2006. pdf
  8. Hyperpolar homogeneous foliations on symmetric spaces of noncompact type. Proceedings of the 13th International Workshop on Differential Geometry and Related Fields, 37-57, Natl. Inst. Math. Sci. (NIMS), Taejon, 2009. arXiv:0912.4408.
  9. A note on hypersurfaces in symmetric spaces. Proceedings of the 14th International Workshop on Differential Geometry and the 3rd KNUGRG-OCAMI Differential Geometry Workshop, 31-41, Natl. Inst. Math. Sci. (NIMS), Taejon, 2010. pdf
  10. Polar actions on symmetric spaces. Proceedings of the 15th International Workshop on Differential Geometry and the 4th KNUGRG-OCAMI Differential Geometry Workshop, 1-10, Natl. Inst. Math. Sci. (NIMS), Taejon, 2011. pdf
  11. Contact hypersurfaces in Kähler manifolds. Proceedings of the 17th International Workshop on Differential Geometry and the 7th KNUGRG-OCAMI Differential Geometry Workshop, 1-11, Natl. Inst. Math. Sci. (NIMS), Taejon, 2013. pdf
  12. Totally geodesic submanifolds of Riemannian symmetric spaces. Real and complex submanifolds, 33-42, Springer Proc. Math. Stat., 106, Springer, Tokyo, 2014. Link to paper
  13. Real hypersurfaces in Hermitian symmetric spaces. Proceedings of the 22nd International Workshop on Differential Geometry of Submanifolds in Symmetric Spaces and the 17th RIRCM-OCAMI Joint Differential Geometry Workshop, 37-46, Kyungpook Natl. Univ., Taegu, 2019.

CONFERENCE PROCEEDINGS
  1. Real and complex submanifolds, ICM2014 Satellite Conference, Daejeon, Korea (edited with Byung Hak Kim, Hyunjin Lee, Yoshihiro Ohnita and Young Jin Suh), Springer Proceedings in Mathematics and Statistics 106, Springer, 2014, 476 pp. ISBN 978-4-431-55214-7.

MONOGRAPHS
  1. Über Untermannigfaltigkeiten von komplexen Raumformen (On submanifolds of complex space forms), Ph.D. Thesis, University of Cologne, Germany, 1989, 107 pp. pdf
  2. A new approach to the complex Grassmann manifolds CG2,m, Habilitation Thesis, University of Cologne, Germany, 1994, 79 pp.

LECTURE NOTES
  1. Lie group actions on manifolds, Lecture notes of a graduate course given at Sophia University, Tokyo, October 2002, 59 pp. pdf

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Last update: 23 April 2023