Andrzej Derdzinski

Professor of Mathematics

Teaching

Summer Quarter 2008:

Math 654 (Complex Variables),    syllabus, course description, additional notes and homework

Recent publications

• On compact manifolds admitting indefinite metrics with parallel Weyl tensor (with Witold Roter), 24 pages, Journal of Geometry and Physics (2008). 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. 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. 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. 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)
  

Preprints

• Totally real immersions of surfaces (with Tadeusz Januszkiewicz), 62 pages.
• Compact pseudo-Riemannian manifolds with parallel Weyl tensor (with Witold Roter), 19 pages.
• The local structure of conformally symmetric manifolds (with Witold Roter), 12 pages, to appear in  Bulletin of the Belgian Mathematical Society - Simon Stevin.
• Connections with skew-symmetric Ricci tensor on surfaces, 23 pages, to appear in  Results in Mathematics - Resultate der Mathematik.
  

Some old papers, 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).
• 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 (pdf file from JSTOR). 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.
• 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

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. 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).
• 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.
• Geometry of the Standard Model, notes of a talk at the Conference on Geometry in Bedlewo, Poland, September 2002 (organized by Th. Friedrich, B. Hajduk and T. Januszkiewicz), 4 pages.