Publications of Jürgen Berndt


BOOKS
  1. Generalized Heisenberg groups and Damek-Ricci harmonic spaces (with Franco Tricerri and Lieven Vanhecke), Lecture Notes in Math., 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 Res. Notes Math., 434, Chapman & Hall/CRC, Boca Raton, FL, 2003, x+336 pp. ISBN: 1-58488-371-5.
  3. Submanifolds and holonomy (with Sergio Console and Carlos Enrique Olmos), Monogr. Res. Notes Math., 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), Adv. Anal. Geom., 5, De Gruyter, Berlin, 2022, xi+373 pp. ISBN 978-3-11-068978-5; 978-3-11-068983-9; 978-3-11-068991-4.

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), Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), no. 4, 343-358.
  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), Math. Publ., 1, Silesian University at Opava, Opava, 1993, 353-364. ISBN: 80-901581-0-2.
  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 M. Woodward), World Scientific Publishing Co., Inc., River Edge, NJ, 1993, 26-40. ISBN: 981-02-1535-5.
  10. Geometry of generalized Heisenberg groups and their Damek-Ricci harmonic extensions (with Franco Tricerri and Lieven Vanhecke), C. R. 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 Hopf hypersurfaces in the nearly Kähler 6-sphere (with John Bolton and Lyndon M. 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, 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.
  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 László Verhóczki), 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), Surv. Differ. Geom., 8, International Press, Somerville, MA, 2003, 1-27. ISBN: 1-57146-114-0.
  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). National Institute for Mathematical Sciences (NIMS), Taejon, 2012, 1-9.
  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), no. 11, 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), Comm. Anal. Geom. 31 (2023), no. 5, 1079-1123.

SURVEY ARTICLES
  1. Real hypersurfaces with constant principal curvatures in complex space forms, World Scientific Publishing Co., Inc., Teaneck, NJ, 1990, 10-19. ISBN: 981-02-0251-2.
  2. Aspects of the geometry of the Jacobi operator (with Lieven Vanhecke), Riv. Mat. Univ. Parma (5) 3 (1994), no. 1, 91-108 (1995).
  3. On curvature and submanifolds of complex two-plane Grassmannians, Kyungpook National University, Basic Science Research Institute, Taegu, 1998, 1-15.
  4. On homogeneous hypersurfaces in Riemannian symmetric spaces, Kyungpook National University, Basic Science Research Institute, Taegu, 1998, 17-34.
  5. Geometry of weakly symmetric spaces, Transilvania University Press, Brasov, 2000, 66-73,
  6. Symmetric submanifolds of symmetric spaces, Kyungpook National University, Department of Mathematics, Taegu, 2003, 1-15.
  7. Real hypersurfaces with constant principal curvatures in complex space forms, Kyungpook National University, Taegu, 2006, 1-12.
  8. Hyperpolar homogeneous foliations on symmetric spaces of noncompact type, National Institute for Mathematical Sciences (NIMS), Taejon, 2009, 37-57.
  9. A note on hypersurfaces in symmetric spaces, National Institute for Mathematical Sciences (NIMS), Taejon, 2010, 31-41.
  10. Polar actions on symmetric spaces, National Institute for Mathematical Sciences (NIMS), Taejon, 2011, 1-10.
  11. Contact hypersurfaces in Kähler manifolds, National Institute for Mathematical Sciences (NIMS), Taejon, 2013, 1-11.
  12. Totally geodesic submanifolds of Riemannian symmetric spaces, Springer Proc. Math. Stat., 106, Springer, Tokyo, 2014, 33-42.
  13. Real hypersurfaces in Hermitian symmetric spaces, Kyungpook National University, Taegu, 2019, 37-46.
  14. Foliated Hopf hypersurfaces in complex hyperbolic quadrics, Kyungpook National University, Taegu, 2023, 393-402.

CONFERENCE PROCEEDINGS
  1. Real and complex submanifolds (edited with Byung Hak Kim, Hyunjin Lee, Yoshihiro Ohnita and Young Jin Suh), Springer Proc. Math. Stat., 106, Springer, Tokyo, 2014, xii+526 pp. ISBN: 978-4-431-55215-4; 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.
  2. A new approach to the complex Grassmann manifolds CG2,m, Habilitation Thesis, University of Cologne, Germany, 1994, 79 pp.

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Last update: 10 October 2025