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)
Departmental fax: (614) 292-1479
E-mail: andrzej(the at symbol)math.ohio-state.edu
Teaching
Preprints
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, to appear in Advances in
Geometry.
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
- Walkers 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
spinc-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)
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).
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.
Last updated on August 11th, 2024.