**Special
geometries and related structures**

CNCS grant PN-III-P4-ID-PCE-2016-0019 contract no. 117/ 2017

**Abstract:
**The
project will bring his contribution in modern differential geometry
and its interplay with complex geometry, theoretical physics and
algebraic geometry.

**Project
coordinator **

� Dr. Liana David , Scientific Researcher I at Institute of Mathematics " Simion Stoilow " of the Romanian Academy

**Research
team (in alphabetical order) **

� Master student Mircea Andrei Florea

� Master student Ionut-Alexandru Hurjui

**Phase one of the
project (12.07-2017-30.12.2017) **

**Expected
results in: **generalized
complex geometry, meromorphic connections, harmonic maps.

**Scientific
report: **link

**Scientific
paper **

�
V.
Cortes, **L.
David **:
*Twist,
elementary deformation, and the KK correspondence in generalized
complex geometry*, Int. J. Math. to appear; arXiv:1706.05516v2
[math.DG]

**Presentations
as Invited Speakers **

� Monica Aprodu: Workshop "Mathematics, Computer Science and Applications", Galaţi, Romania, December 2017.

� Costin Vîlcu: International Symposium on Discrete and Convex Geometry, Shijiazhuang, China, December 2017.

**Research
Visits Abroad **

� Monica Aprodu: University of Genoa (Italy), (5 days) September 2017.

� Liana David: University of Mannheim (Germany), (18 days) October - November 2017.

� Radu Pantilie: Université de Brest (France), (13 days) December 2017.

**Phase two of the
project **

**Expected
results in: **quaternionic
and quaternionic-Kahler geometry, special Kahler geometry, harmonic
maps, meromorphic connections.

**Scientific
report: **link

**Scientific
papers **

�
**M.
A. Aprodu **:
*Harmonic
non-holomorphic maps from S² to Hirzebruch surfaces*,
sent for publication

�
**
L. David, **
C. Hertling :
*
(T)-structures over 2-dimensional F-manifolds: formal classification
*,
Annali di Matematica Pura ed Applicata, to appear; arXiv:1811.03406
[math.DG]

�
**R.
Pantilie **:
*Projective
structures and ρ-connections*,
J. Inst. Math.
Jussieu 19 (2020), 571-579

�
**R.
Pantilie **:
*Harmonic
morphisms and the Penrose-Ward transform*,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 30 (1), 2019,
175-194

�
A.
Rivière, J. Rouyer, **C.
Vîlcu**,
T.
Zamfirescu : *Double
normals of most convex bodies*,
Adv.
in Math. 343 (2019), 245-272; arXiv:1804.07015
[math.MG]

**Presentations
as Invited Speakers **

� Liana David: Workshop "Special Metrics and Symmetries on Complex Manifolds", Universitaty of Regensburg, Germany, 10-15 September, 2018.

� Radu Pantilie: The Differential Geometry Workshop 2018, Università di Cagliari, Italy, 12-14 September, 2018.

� Monica Aprodu: Workshop "Mathematics, Computer Science and Applications", University "Dunărea de Jos" of Galaţi, Romania, December 2018.

**Research
Visits Abroad **

� Liana David: University of Hamburg (Germany), (6 days) September 2018.

**
Phase three of the project **

**
Expected results in: **
quaternionic and quaternionic-Kahler geometry, harmonic maps, singular spaces.

**
Scientific report: **
link

**
Scientific papers **

�
**
R. Pantilie **
:
*
On the embeddings of the Riemann sphere with nonnegative normal bundles*,
Electron.
Res. Announc. Math. Sci. 25 (2018) 87–95;
arXiv:1307.1993v3
[math.DG]

�
G.
Deschamps, E. Loubeau,
**
R. Pantilie
**
:
*
Harmonic maps and twistorial structures,*
Mathematika 66 (2020) 112–124;
arXiv:1804.05423
[math.DG]

�
V.
Cortés, **L.
David **:
*Generalized
connections, spinors, and integrability of generalized structures on
Courant algebroids*,
sent for publication; arXiv:1905.01977v2
[math.DG]

�
**
L. David,
**
C. Hertling:
*
(TE)-structures over the irreducible 2-dimensional globally nilpotent F-manifold germ,
*
Rev. Roum. Math. Pure Appl., to appear;
arxiv:2001.01063 [math.DG], 53 pages

�
J. Itoh, **
C. Vîlcu**,
T. Zamfirescu : *With respect to whom are you critical?*,
Adv. in Math. 369 (2020) 107187;
arXiv:1903.10908 [math.GT]

� Several papers are still in progress. Details about them are presented in the scientific report for the period 2017 - September 2019.

**
Presentations as Invited Speakers **

� Liana David: Workshop on Riemannian and Kähler Geometry, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Romania, 15-19 April, 2019.

� Liana David: The Ninth Congress of Romanian Mathematicians, University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

� Costin Vîlcu: The Ninth Congress of Romanian Mathematicians, University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

� Costin Vîlcu: International Symposium on Convexity and Discrete Geometry, Hebei Normal University, China, 25 - 30 August, 2019.

� Monica Aprodu was a member in the organizing committee of the "Ninth Congress of Romanian Mathematicians", University "Dunărea de Jos" of Galaţi, Romania, June 28 - July 3, 2019.

**Research
Visits of Foreign Mathematicians **

� Prof. Vicente Cortés from University of Hamburg (Germany) visited IMAR during September 2 -8, 2019, in order to participate at the workshop "Geometry and Physics" organized at IMAR during this period, and to collaborate with Liana David on topics of the project (about generalized geometry).