Andrzej Derdzinski

Professor of Mathematics

Teaching

Autumn Semester 2024:

Math 6701 (Differentiable Manifolds)    syllabus, course description, additional notes and homework

Math 2568 (Linear Algebra)

Preprints

• Nijenhuis geometry of parallel tensors (with Paolo Piccione and Ivo Terek), 21 pages.
• Special Ricci-Hessian equations on Kähler manifolds (with Paolo Piccione), 18 pages.

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Publications, 2020 - 2024

• Harmonic curvature in dimension four, 34 pages, to appear in Journal of the Korean Mathematical Society.
• Compact flat manifolds and reducibility (with Paolo Piccione), 27 pages, to appear in Advances in Submanifold Theory and Related Topics, a special volume of Latin American Mathematics Series - UFSCar subseries in honor of Marcos Dajczer's 75th birthday.
• Harmonic-curvature warped products over surfaces (with Paolo Piccione), 23 pages, to appear in Communications in Analysis and Geometry, vol. 32 (2024), no. 9.
• Compact locally homogeneous manifolds with parallel Weyl tensor (with Ivo Terek), 15 pages, Advances in Geometry, vol. 24 (2024), no. 4, pp. 493–503. DOI: 10.1515/advgeom-2024-0019
• Rank-one ECS manifolds of dilational type (with Ivo Terek), 26 pages, Portugaliae Mathematica, vol. 81 (2024), no. 1/2, pp. 69-96. DOI: 10.4171/PM/2110
• Killing fields on compact pseudo-Kähler manifolds (with Ivo Terek), 7 pages, Journal of Geometric Analysis, vol. 34 (2024), no. 5, art. 144. DOI: 10.1007/s12220-024-01591-z
• New examples of compact Weyl-parallel manifolds (with Ivo Terek), 13 pages, Monatshefte für Mathematik, vol. 203 (2024), no. 4, pp. 859-871. DOI: 10.1007/s00605-023-01908-0
• The metric structure of compact rank-one ECS manifolds (with Ivo Terek), 20 pages, Annals of Global Analysis and Geometry, vol. 64 (2023), no. 4, art. 24. DOI: 10.1007/s10455-023-09929-6
• Compact Weyl-parallel manifolds, 5 pages, Romanian Journal of Mathematics and Computer Science, vol. 13 (2023), no. 2, pp. 1-5. Special Issue  Proceedings of the International Conference Riemannian Geometry and Applications - RIGA 2023
• The topology of compact rank-one ECS manifolds (with Ivo Terek), 22 pages, Proceedings of the Edinburgh Mathematical Society, vol. 66 (2023), no. 3, pp. 789-809. DOI: 10.1017/S0013091523000408
• Null-projectability of Levi-Civita connections (with Kirollos Masood), 15 pages, Results in Mathematics - Resultate der Mathematik, vol. 78 (2023), no. 4, art. 141. DOI: 10.1007/s00025-023-01911-9
• Subspace foliations and collapse of closed flat manifolds (with Renato G. Bettiol, Roberto Mossa and Paolo Piccione), 23 pages, Mathematische Nachrichten, vol. 295 (2022), no. 12, pp. 2338-2356. DOI: 10.1002/mana.202000156
• Maximally-warped metrics with harmonic curvature (with Paolo Piccione), 13 pages, in: Geometry of Submanifolds, proceedings of an AMS special session in honor or Bang-Yen Chen's 75th birthday, held at the University of Michigan, Ann Arbor, MI, October 20-21, 2018, edited by J. Van der Veken, A. Carriazo, I. Dimitrić, Y. M. Oh, B. D. Suceavă and L. Vrancken, Contemporary Mathematics, vol. 756, American Mathematical Society, Providence, RI, 2020, pp. 83-96. DOI: 10.1090/conm/756/15198
• Kähler manifolds with geodesic holomorphic gradients (with Paolo Piccione), 38 pages, Revista Matemática Iberoamericana, vol. 36 (2020), no. 5, pp. 1489-1526 (online-first pdf file from EMS). DOI: 10.4171/rmi/1173
  

Publications, 2010 - 2018

• Teichmüller theory and collapse of flat manifolds (with Renato G. Bettiol and Paolo Piccione), 16 pages, Annali di Matematica Pura ed Applicata, vol. 197 (2018), no. 4, pp. 1247-1268. DOI: 10.1007/s10231-017-0723-7
• Witold Roter (1932-2015), 8 pages, Colloquium Mathematicum, vol. 150 (2017), no. 1, pp. 1-8. DOI: 10.4064/cm7409s-9-2017
• O dorobku naukowym Witolda Rotera, 15 pages, Wiadomości Matematyczne, vol. 52 (2016), no. 2, pp. 299-313. DOI: 10.14708/wm.v52i2.3299
• Indefinite Einstein metrics on simple Lie groups (with Światosław R. Gal), 43 pages, Indiana University Mathematics Journal, vol. 63 (2014), no. 1, pp. 165-212. DOI: 10.1512/iumj.2014.63.5191
• Curvature spectra of simple Lie groups (with Światosław R. Gal), 12 pages, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 83 (2013), no. 2, pp. 219-230. DOI: 10.1007/s12188-013-0085-z
• Killing potentials with geodesic gradients on Kähler surfaces, 21 pages, Indiana University Mathematics Journal, vol. 61 (2012), no. 4, pp. 1643-1666. DOI: 10.1512/iumj.2012.61.4687
• Special biconformal changes of Kähler surface metrics, 16 pages, Monatshefte für Mathematik, vol. 167 (2012), no. 3-4, pp. 431-448. DOI: 10.1007/s00605-011-0345-x
• Two-jets of conformal fields along their zero sets, 16 pages, Central European Journal of Mathematics, vol. 10 (2012), no. 5, pp. 1698-1709. DOI: 10.2478/s11533-012-0049-z
• Ricci solitons, 32 pages, English translation of Solitony Ricciego, Wiadomości Matematyczne, vol. 48 (2012), no. 1, pp. 1-32 (pdf file from PTM). URL: http://wydawnictwa.ptm.org.pl/index.php/wiadomosci-matematyczne/article/view/211 DOI: 10.14708/wm.v48i1.211
• Zeros of conformal fields in any metric signature, 26 pages, Classical and Quantum Gravity, vol. 28 (2011), no. 7, 075011. DOI: 10.1088/0264-9381/28/7/075011
• Noncompactness and maximum mobility of type III Ricci-flat self-dual neutral Walker four-manifolds, 31 pages, The Quarterly Journal of Mathematics, vol. 62 (2011), no. 2, pp. 363-395. DOI: 10.1093/qmath/hap033
• Totally real immersions of surfaces (with Tadeusz Januszkiewicz), 62 pages, Transactions of the American Mathematical Society, vol. 362 (2010), no. 1, pp. 53-115. DOI: 10.1090/S0002-9947-09-04940-X
• Compact pseudo-Riemannian manifolds with parallel Weyl tensor (with Witold Roter), 19 pages, Annals of Global Analysis and Geometry, vol. 37 (2010), no. 1, pp. 73-90. DOI: 10.1007/s10455-009-9173-9
  

Publications, 2003 - 2009

• Non-Walker self-dual neutral Einstein four-manifolds of Petrov type III, 47 pages, Journal of Geometric Analysis, vol. 19 (2009), no. 2, pp. 301-357. DOI: 10.1007/s12220-008-9066-3
• The local structure of conformally symmetric manifolds (with Witold Roter), 12 pages, Bulletin of the Belgian Mathematical Society - Simon Stevin, vol. 16 (2009), no. 1, pp. 117-128. DOI: 10.36045/bbms/1235574196
• Connections with skew-symmetric Ricci tensor on surfaces, 23 pages, Results in Mathematics - Resultate der Mathematik, vol. 52 (2008), no. 3-4, pp. 223-245. DOI: 10.1007/s00025-008-0307-3
• On compact manifolds admitting indefinite metrics with parallel Weyl tensor (with Witold Roter), 24 pages, Journal of Geometry and Physics, vol. 58 (2008), no. 9, pp. 1137-1147. DOI: 10.1016/j.geomphys.2008.03.011
• Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds (with Witold Roter), 40 pages, Tohoku Mathematical Journal, vol. 59 (2007), no. 4, pp. 565-602 (open-access pdf file). DOI: 10.2748/tmj/1199649875
• Global properties of indefinite metrics with parallel Weyl tensor (with Witold Roter), 10 pages, in: Pure and Applied Differential Geometry - PADGE 2007, edited by F. Dillen and I. Van de Woestyne, in the series Berichte aus der Mathematik, Shaker Verlag, Aachen, 2007, pp. 63-72.
• Special Kähler-Ricci potentials on compact Kähler manifolds (with Gideon Maschler), 44 pages, Journal für die reine und angewandte Mathematik, vol. 593 (2006), pp. 73-116. DOI: 10.1515/CRELLE.2006.030
• Walker’s theorem without coordinates (with Witold Roter), 8 pages, Journal of Mathematical Physics, vol. 47 (2006), no. 6, 062504, 8 pp. (pdf file from AIP). DOI: 10.1063/1.2209167
• A Myers-type theorem and compact Ricci solitons, 4 pages, Proceedings of the American Mathematical Society, vol. 134 (2006), no. 12, pp. 3645-3648 (open-access pdf file). DOI: 10.1090/S0002-9939-06-08422-X
• A moduli curve for compact conformally-Einstein Kähler manifolds (with Gideon Maschler), 52 pages, Compositio Mathematica, vol. 141 (2005), no. 4, pp. 1029-1080 (open-access pdf file). DOI: 10.1112/S0010437X05001612
• Immersions of surfaces in spin^c-manifolds with a generic positive spinor (with Tadeusz Januszkiewicz), 25 pages, Annals of Global Analysis and Geometry, vol. 26 (2004), no. 2, pp. 175-199 and no. 3, p. 319. DOI: 10.1023/B:AGAG.0000031163.94882.de
• Local classification of conformally-Einstein Kähler metrics in higher dimensions (with Gideon Maschler), 41 pages, Proceedings of the London Mathematical Society (3), vol. 87 (2003), no. 3, pp. 779-819. DOI: 10.1112/S0024611503014175
• Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case, 18 pages, in: Recent Advances in Riemannian and Lorentzian Geometries, proceedings of an AMS special session held at Baltimore, MD, January 15-18, 2003, edited by K. L. Duggal and R. Sharma, Contemporary Mathematics, vol. 337, American Mathematical Society, Providence, RI, 2003, pp. 21-38 (accessible at books.google.com). DOI: 10.1090/conm/337/06049
  

Some old papers, notes and preprints accessible on line

• Self-dual Kähler manifolds and Einstein manifolds of dimension four, 29 pages, Compositio Mathematica, vol. 49 (1983), no. 3, pp. 405-433 (pdf file from NUMDAM). DOI: http://www.numdam.org/item?id=CM_1983__49_3_405_0
• Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, 8 pages, Mathematische Zeitschrift, vol. 172 (1980), no. 3, pp. 273-280 (pdf file from GDZ). DOI: 10.1007/BF01215090
• Exemples de métriques de Kähler et d'Einstein auto-duales sur le plan complexe, 13 pages, in: Géométrie riemannienne en dimension 4, Séminaire Arthur Besse 1978/79, Cedic/Fernand Nathan, Paris, 1981, pp. 334-346.
• On compact Riemannian manifolds with harmonic curvature, 6 pages, Mathematische Annalen, vol. 259 (1982), no. 2, pp. 145-152 (pdf file from GDZ). DOI: 10.1007/BF01457307
• Codazzi tensor fields, curvature and Pontryagin forms (with C.-L. Shen), 12 pages, Proceedings of the London Mathematical Society (3), vol. 47 (1983), no. 1, pp. 15-26 (pdf file from LMS). DOI: 10.1112/plms/s3-47.1.15
• Unflat connections in 3-sphere bundles over  S⁴ (with A. Rigas), 9 pages, Transactions of the American Mathematical Society, vol. 265 (1981), no. 2, pp. 485-493 (open-access pdf file). DOI: 10.2307/1999745
• On conformally symmetric manifolds with metrics of indices 0 and 1 (with W. Roter), 5 pages, Tensor, New Series, vol. 31 (1977), no. 3, pp. 255-259.
• Compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, 3 pages, in: Global Differential Geometry and Global Analysis, proceedings of the colloquium held at the Technical University of Berlin, November 21 - 24, 1979, Lecture Notes in Mathematics, vol. 838 (1981), pp. 126-128. DOI: 10.1007/BFb0088848
• A lower bound for  λ₁ on manifolds with boundary (with C. B. Croke), 16 pages, Commentarii Mathematici Helvetici, vol. 62 (1987), no. 1, pp. 106-121 (pdf file from GDZ). DOI: 10.1007/BF02564440
• Hermitian Einstein metrics, 10 pages, in: Global Riemannian Geometry, edited by T. J. Willmore and N. Hitchin, Ellis Horwood Ltd., Chichester, 1984, pp. 105-114.
• Some theorems on conformally symmetric manifolds (with W. Roter), 11 pages, Tensor, New Series, vol. 32 (1978), no. 1, pp. 11-23.
• A condition for positivity of curvature (with L. M. Chaves and A. Rigas), 13 pages, Boletim da Sociedade Brasileira de Matemática, vol. 23 (1992), no. 1-2, pp. 153-165. DOI: 10.1007/BF02584817
• Riemannian metrics with harmonic curvature on 2-sphere bundles over compact surfaces, 24 pages, Bulletin de la Société mathématique de France, vol. 116 (1988), no. 2, pp. 133-156 (pdf file from NUMDAM).
• Riemannian manifolds with harmonic curvature, 12 pages, in: Global Differential Geometry and Global Analysis 1984, proceedings of a conference held in Berlin, June 10 - 14, 1984,  Lecture Notes in Mathematics, vol. 1156 (1985), pp. 74-85. DOI: 10.1007/BFb0075087
• Some remarks on the local structure of Codazzi tensors, 5 pages, in: Global Differential Geometry and Global Analysis, proceedings of the colloquium held at the Technical University of Berlin, November 21 - 24, 1979, Lecture Notes in Mathematics, vol. 838 (1981), pp. 251-255. DOI: 10.1007/BFb0088867
• Vorlesung Differentialgeometrie, Bonn, 1983-1984, lecture notes, 796 pages, plus Aufgabenlisten, 76 pages
• Sobolew-Räume, Bonn, 1983, lecture notes, 142 pages
• An easy construction of new compact Riemannian manifolds with harmonic curvature, 10 pages, Max-Planck-Institut für Mathematik, preprint 1983-21, Bonn, 1983 (pdf file from MPI)
  

Chapters in books on differential geometry

• Generalizations of the Einstein condition, Chapter 16 of the Arthur L. Besse book Einstein Manifolds, in the series Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 10, Springer-Verlag, 1987, pp. 432-455. DOI: 10.1007/978-3-540-74311-8_17
• Einstein metrics in dimension four, Chapter 4 of Handbook of Differential Geometry, Vol. I (edited by F.J.E. Dillen and L.C.A. Verstraelen), Elsevier Science B.V., 2000, pp. 419-707. DOI: 10.1016/S1874-5741(00)80007-2. Click here for a two-page list of corrections.
  

Writings on particle physics

• Geometry of the Standard Model of Elementary Particles, a book in the series Texts and Monographs in Physics, Springer-Verlag, 1992 (xii + 199 pp., ISBN 3-540-54356-2). DOI: 10.1007/978-3-642-50310-8
• Geometry of elementary particles, in: Proceedings of Symposia in Pure Mathematics, vol. 54, 1993 (edited by R. E. Greene and S.-T. Yau), Part 2, pp. 157-171 (accessible at books.google.com). This is a 14-page summary of the book listed above. DOI: 10.1090/pspum/054.2/1216535
• Geometry of the Standard Model, notes of a talk at the Conference on Geometry in Będlewo, Poland, September 2002 (organized by Th. Friedrich, B. Hajduk and T. Januszkiewicz), 4 pages.