Johann Todorov Davidov 
Personal Data  

Address 
“Lyuben Karavelov” Civil Engineering Higher School, 
Telephone 
(+359 2) 80 29 124 

jtd@math.bas.bg 
Education  
1978 
Ph. D. in Mathematics 
1972 
M. Sc. in Mathematics, University of Sofia, Sofia, Bulgaria 
Professional experience  
2004 
Doctor of Mathematical Sciences 

“L. Karavelov” Civil Engineering Higher School, Sofia, Bulgaria 
2009 
Professor 

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences 
2005 
Professor 
19892005 
Associate Professor 
19781989 
Assistant Professor 

University of Veliko Tarnovo, Bulgaria 
19902000 20062007 
Adjunct Professor


University of Sofia, Bulgaria 
1978 19711978 
Adjunct Professor Teaching Assistant 

Higher Institute of Civil Engineering and Architecture, Sofia, Bulgaria 
19751977 
Adjunct Faculty 

Abdus Salam Scool of Mathematical Sciences, GC University, Lahore, Pakistan 
2009 
Visiting Lecturer 

Florida International University, Department of Mathematics, Miami, USA 
20072008 
Visiting Lecturer 

MaxPlanckInstitut für Mathematik, Bonn, Germany 
20022003 
Visiting Scholar 

Michigan State University, Department of Mathematics, East Lansing, USA 
2000, 2001 
Visiting Scholar under NSFgrant INT9903302 

Mathematisches Forschungsinstitut, Oberwolfach, Germany 
1995, 1997, 2000 
Visiting Scholar under the Research in Pair Programme 

Middle East Technical University, Department of Mathematics, Ankara, Turkey 
1998 
Visiting Scholar 

International Centre for Theoretical Physics, Trieste, Italy 
1990 
Visiting Scholar 

International research grants and projects 
19992002 
Geometry of fourmanifolds and twistor spaces, NSF grant INT9903302 (investigatorcoordinator from the Bulgarian side) 
2002004 
European Differential Geometry Endeavor, Research Training Network HPRNCT 200000101, supported by the European Human Potential Programme 
19962001, 20062007, 20092011, 2012 
Complex analysis, complex geometry and mathematical physics, joint research project with the Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow, Russia (investigatorcoordinator from the Bulgarian side in the period 20062007 and 2009present 

National research projects 
20092011 
Geometry of Riemannian manifolds with special structures, “L. Karavelov” Civil Engineering Higher School, Sofia, Bulgaria 

Research interests 

Differential Geometry: twistor spaces, almostcomplex manifolds, almostcontact manifolds, selfdual manifolds, Hermitian surfaces, harmonic maps Complex Analysis: invariant pseudometrics  Bergman, Kobayashi, Carathéory 

Teaching experience 

Undergraduate courses: Calculus, Real analysis, Complex analysis, Differential geometry of curves and surfaces, Linear algebra, College algebra, Descriptive geometry. Graduate courses: Harmonic and holomorphic maps, Bundles and connections, Several complex variables, dbar problem, Introduction to smooth manifolds, Calculus on manifolds Supervision of graduate students: Supervised 5 M.S. and 3 Ph.D. 

Membership in professional organizations 

American Mathematical Society, Union of Bulgarian Mathematicians 

Other professional activities 
2010 
Member of the General Assembly of the Bulgarian Academy of Sciences 
2009 
Chairman of the General Assembly of Scientists, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. 
2008 
Member of the Scientific Council of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences 
20062010 
Member of the Commission on Mathematics, High Testimonial Committee of Bulgaria (2009 and 2010  Secretary of the Commission) 
19922000 
Member of the Scientific Council of the Department of Mathematics and Informatics, University of Veliko Tarnovo 
2006 
Member of the Editorial Board of JP Journal of Geometry and Topology 
2012 
Member of the Editorial Board of Mathematical Sciences and Applications ENotes 
1981 
Reviewer for Mathematical Reviews 
1979 
Reviewer for Zentralblatt für Mathematik 

Languages 

English, Russian, French, German, Bulgarian  native 
On a Principle of Compactness and Generalization of Certain Theorems of H.Cartan and Carathéodory, Comp. Rend. Acad. Bulg. Sci., 29, no.1 (1976), 923926.
The Representative Domain of a Complex Manifold and the LuQiKeng Conjecture, Comp. Rend. Acad. Bulg. Sci., 30, no.1 (1977), 1316.
On the Infinitesimal Transformations of a Bounded Circular Domain in , Compt. Rend. Acad. Bulg. Sci., 30, no.12 (1977), 16811684.
Bounded Families of Holomorphic Mappings between Complex Manifolds, Serdica, 5 (1979), 173178.
Representative Domains of Complex Manifolds, Pliska, Studia Mathematica Bulgarica, 4 (1981), 3657.
Бележка върху принципа за компактност (English summary), Mathematics and Education in Mathematics, Proceedings of the 11th Spring Conference of the Union of Bulgarian Mathematicians, 1982, 161165.
Examples of Typical Carathéodory and Kobayashi Pseudodistances, Compt. Rend. Acad. Bulg. Sci., 39, no.1 (1985), 2325. (with V. Hristov)
Note on the Extendability of Holomorphic Mappings into Complex Manifolds, Mathematics and Education in Mathematics, Proceedings of the 15th Spring Conference of the Union of Bulgarian Mathematicians, 1986, 208215.
Existence of Holomorphic Functions on Twistor Spaces, Bull. Soc. Math. Belgique, 40, fasc. Iser. B (1989), 131151. (with O. Mushkarov)
Twistor Spaces with Hermitian Ricci Tensor, Proc. Amer. Math. Soc., 109, no.4 (1990), 11151120. (with O. Mushkarov)
On the Riemannian Curvature of a Twistor Space, Acta Math. Hungarica, 58, no.34 (1991), 319332. (with O. Mushkarov)
Twistor Spaces and Harmonic Maps (in Russian), Uspehi Mat. Nauk, 48, no.3 (1993), 396; English translation in Russian Math. Surveys, 48, no.3 (1993), 191. (with A. Sergeev)
Twistor Spaces and Their Applications in Differential Geometry, Mathematics and Education in Mathematics, Proceedings of the 23rd Spring Conference of the Union of Bulgarian Mathematicians, 1994, 5483. (with O. Mushkarov)
Almost Complex Structures on Twistor Spaces, in K.Sekigawa, S.Dimiev (Editors), Almost Complex Structures, Proceedings of the International Workshop held in Sofia, August 2025, 1992, World Scientific, 1994, 113149. (with G. Grantcharov and O. Mushkarov)
Kähler Curvature Identities for Twistor Spaces, Illinois J. Math., 39, no.4 (1995), 627634. (with G. Grantcharov and O. Mushkarov)
Compact SelfDual Hermitian Surfaces, Trans. Amer. Math. Soc., 348, no.8 (1996), 30513063. (with V. Apostolov and O. Mushkarov)
Geometry of Hermitian Surfaces, in S.Dimiev, K.Sekigawa (Editors), Topics in Complex Analysis, Differential Geometry and Mathematical Physics, Proceedings of the 3rd International Workshop on Complex Structures and Vector Fields held in St.Konstantin, 2329 August, 1996, World Scientific, 1997, 94104. (with V. Apostolov, G. Grantcharov and O. Mushkarov)
Twistor Quantization of Loop Spaces (in Russian), Proceedings of the Steklov Institute of Mathematics, 217 (1997), 599, English translation, pp. 196. (with A. Sergeev)
Compact Hermitian Surfaces and Isotropic Curvature, Illinois J. Math., 44 (2000), 438450. (with V. Apostolov)
Twistorial Examples of *Einstein Manifolds, Ann. Glob. Anal. Geom., 20 (2001), 103115. (with G. Grantcharov and O. Mushkarov)
Twistorial Examples of Almost Contact Metric Manifolds, Houston J. Math., 28, no.4 (2002), 711740.
Harmonic AlmostComplex Structures on Twistor Spaces, Israel J. Math., 131 (2002), 319332. (with O. Mushkarov)
Almost Contact Metric Structures and Twistor Spaces, Houston J. Math., 29, no.3 (2003), 639674.
Isotropic Kähler Hyperbolic Twistor Spaces, J. Geom. Phys., 52 (2004), 7488. (with D. Blair and O. Mushkarov)
Einstein Condition and Twistor Spaces of Compatible Partially Complex Structures, Diff. Geom. and its Appl., 22 (2005), 159179.
Hyperbolic Twistor Spaces, Rocky Mountain J. Math., 35 (2005), 14371465. (with D. Blair and O. Mushkarov)
EtaEinstein Condition on Twistor Spaces of OddDimensional Riemannian Manifolds, J. Geom., 86 (2006), 4253.
Curvature Properties of the Chern Connection of Twistor Spaces, Rocky Mountain J. Math., 39 (2009), 2748. (with G. Grantcharov and O. Mushkarov)
Twistor Spaces of Generalized Complex Structures, J. Geom. Phys., 56 (2006), 16231636. (with O. Mushkarov)
Selfdual Walker Metrics with Twostep Nilpotent Ricci Operator, J. Geom. Phys., 57, no.1 (2006), 157165. (with O. Mushkarov)
Twistorial Construction of Generalized Kähler Manifolds, J. Geom. Phys., 57, no.3 (2007), 889901. (with O. Mushkarov)
Almost Kähler Walker 4Manifolds, J. Geom. Phys., 57, no.3 (2007), 10751088. (with J.C. DíazRamos, E. GarcíaRío, Y. Matsushita, O. Mushkarov and R. VázquezLorenzo)
HermitianWalker 4Manifolds, J. Geom. Phys., 58, no.3 (2008), 307323. (with J.C. DíazRamos, E. GarcíaRío, Y. Matsushita, O. Mushkarov and R. VázquezLorenzo)
Geometry of Neutral Metrics in Dimension Four, Proceedings of the 37th Spring Conference of the Union of Bulgarian Mathematicians, Borovets, April 26, 2008, pp. 3753 (available at arXiv:0804.2132v1 [mathDG] 14 Apr. 2008). (with G. Grantcharov and O. Mushkarov)
Parahyperhermitian Surfaces, Bull. Math. Soc. Sci. Math. Roumanie, 52 (100), no.3 (2009), 281289. (with G. Grantcharov, O. Mushkarov, M. Yotov)
Generalized PseudoKähle Structures, Comm.Math.Phys., 304 (2011), 4968 (with G. Grantcharov, O. Mushkarov, M. Yotov).
The Twistor Space of a Quaternionic Contact Manifolld, Quart. J. Math., (with S. Ivanov, I. Minchev) (to appear)
Parahyperhermitian Structures on Complex Surfaces (with G. Grantcharov and O. Mushkarov) (to appear)
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