Andrzej Derdzinski

Professor of Mathematics

Department of Mathematics
The Ohio State University
231 W. 18th Avenue
Columbus, OH 43210
USA

Office: MW 442 (Math Tower)
Office phone: (614) 292-4012
Departmental fax: (614) 292-1479
E-mail: andrzej(the ‘at’ symbol)math.ohio-state.edu

Teaching

Spring Semester 2019:

Math 3345 (Foundations of Higher Mathematics), M-W-F 11:30 a.m. general information, syllabus, course description

Math 6702 (Differential Geometry), M-W-F 1:50 p.m.

Preprints

Flat manifolds and reducibility (with Paolo Piccione), 23 pages.
Maximally-warped metrics with harmonic curvature (with Paolo Piccione), 12 pages.
Kähler manifolds with geodesic holomorphic gradients (with Paolo Piccione), 52 pages.

Publications, 2010 - present

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: http://projecteuclid.org/euclid.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)

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 (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

Some other old papers in electronic form

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).
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 Będlewo, Poland, September 2002 (organized by Th. Friedrich, B. Hajduk and T. Januszkiewicz), 4 pages.

Last updated on January 7th, 2019.