# Стефан Петров Иванов

Професор
Доктор на науките

### Геометрия

Имейл:
ivanovsp@fmi.uni-sofia.bg
Телефон:
+359 2 8161 780
Кабинет:
ФзФ-05
Приемно време:

вторник 12.05-13.05,
четвъртък - 12.05-13.05

### Образование и научни степени

• Д-р - 1987г.;
• Доктор на математическите науки - 2006г.;
• Доцент на СУ 'Св.Кл.Охридски' - 2000г.;
• Професор на СУ 'Св.Кл.Охридски'- 2008г.;
• Член-кореспондент на БАН-2014г.

### Научни интереси

• Риманова и комплексна диференциална геометрия,
• Ермитови повърхнини и холоморфни векторни разслоения, твисторни пространства, почти Ермитова геометрия,
• Геометрия на почти контактни метрични многообразия,
• Паралелни спинори и опреатори на Дирак, Хармонични изображения,
• Интегруеми системи, системи на Стакел и разделяне не променливите,
• Струнни теории и съответни геометрии, свързаности с торзия и специална холономия,
• Калаби-Яу-тип теорема за компактни Ермитови некелерови 6-мерни многообразия,
• Кватернионна геометрия и кватернионно контактни структури, Кватернионно контактен проблем на Ямабе и ектремали на неравенства от Соболев тип върху кватернионната група на Хайзенберг.

### Преподавателска дейност

Летен семестър учебна 2020-2021 година

• Диференциална Геометрия, спец.  Математика II курс

### Списък с публикации

#### Books

• Extremals of the Sobolev inequality and the quaternionic contact Yamabe problem, (with D. Vassilev), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. xviii+219 pp.
• Quaternionic contact Einstein structures and quaternionic contact Yamabe problem, (with I. Minchev and D. Vassilev), Memoirs Amer. Math. Soc. (2014), 231, no. 1086.

#### Survey papers

• The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds, (with Dimiter Vassilev), Nonlinear Analysis - Theory 126 (2015), 262-323.

#### Papers

• Quaternionic contact hypersurfaces in hyper-K\"ahler manifolds, (with Ivan Minchev, Dimiter Vassilev), to appear in Annali di matematica Pura ed Applicata. arXiv:1406.4256.
• Quaternionic contact Einstein manifolds , (with Ivan Minchev and Dimiter Vassilev), to appear in Math. Research Letters. arXiv:1306.0474.
• Connections on non-symmetric (generalized) Riemannian manifold and gravity, (with Milan Zlatanovic), to appear in Class. Quntum Gravity. arXiv:1503.05217.
• The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven , (with Alexander Petkov and Dimiter Vassilev), to appear in J. Spectral Theory. arXiv:1303.0409.
• The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5 , (with Marisa Fernandez, Luis Ugarte, Dimiter Vassilev), Comm. Math. Phys. 339 (2015), no. 1, 199–219. arXiv:arXiv:1410.4130.
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton , (with Marisa Fernandez, Luis Ugarte, Dimiter vassilev), J. High Energy Physics (JHEP) 06 (2014) 073; arXiv:arXiv:1402.6107.
• Vanishing theorems on $(l|k)$-strong Kaehler manifolds with torsion, (with George Papadopoulos), Adv. Math. 237 (2013), 147-164. arXiv: arXiv:1202.6470 .
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion , (with Dimiter Vassilev), J. Geom 103, 3 (2012), 475-504. arXiv: arXiv:1203.5812.
• An Obata-type theorem on a three-dimensional CR manifold,(with Dimiter Vassilev), Glasgow Math. J., 56 (2014), 283-294. arXiv: arXiv:1208.1040.
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven (with Alexander Petkov and Dimiter Vassilev), Nonlinear Analysis-Theory, 93 (2013), 51-61. arXiv:arXiv:1210.6932.
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold , (with Alexander Petkov and Dimiter Vassilev), J. Geom. Analysis, 24 (2014), no. 2, 595-612. arXiv:arXiv:1112.0779.
• The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group, (with I. Minchev and D. Vassilev), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XI (2012), 635-652; arXiv:arXiv:1009.2978.
• Quaternionic Kaehler and Spin(7) metrics arising from quaternionic contact Einstein structures, (with L. C. de Andres, M. Fernandez, J. A. Santisteban, L. Ugarte and D. Vassilev), Annali di matematica Pura ed Applicata, 193, 1 (2014), 261-290. arXiv:arXiv:1009.2745.
• Bianchi type A hyper-symplectic and hyper-K\"ahler metrics in 4D , (with Luis C. de Andre's, Marisa Ferna'ndez, Jose A. Santisteban, Luis Ugarte and Dimiter Vassilev), Class. Quant. Grav. 29 (2012), 025003. arXiv:arXiv:1102.1518.
• Compact supersymmetric solutions of the heterotic equations of motion in dimensions 7 and 8, (with M. Ferna'ndez, L. Ugarte and R. Villacampa), Adv. Theor. Math. Phys., (2011) 15, 245-284. arXiv:0806.4356.
• HKT manifolds with holonomy SL(n,H), (with A. Petkov), International Mathematics Research Notices, 2012, 16, 3779--3799; arXiv:arXiv:1010.5052.
• The twistor space of a quaternionic contact manifold, (with J. Davidov and I. Minchev), Quart. J. Math. 63 (2012), no. 4, 873-890. arXiv:arXiv:1010.4994.
• Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B685 (2010), 190-196. arXiv:0908.2927.
• Quaternionic contact manifolds with a closed fundamental 4-form, (with D. Vassilev), Bull. London Math. Soc., 42 (6) (2010), 1021–1030. arXiv:0810.3888,.
• Conformal quaternionic contact curvature and the local sphere theorem, (with D. Vassilev), Journal de Mathe'matiques Pures et Applique'es (JMPA) 93 (2010), 277-307. arXiv:0707.1289.
• Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, (with I. Minchev and D. Vassilev), J. Eur. Math. Soc. (JEMS) 12 (2010), 1041–1067. math.DG/0703044
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5, (with M. Ferna'ndez, L. Ugarte and R. Villacampa), Nuclear Physics B820 (2009), 483-502. arXiv:0811.2137.
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton, (with M. Ferna'ndez, L. Ugarte and R. Villacampa), Comm. Math. Phys. 288 (2009), 677-697. arXiv:0804.1648
• Conformal Paracontact curvature and the local flatness theorem, (with D. Vassilev and S. Zamkovoy), Geom. Dedicata 144 (2010), 79-100. arXiv:0707.3773
• Curvature decomposition of $G_2$ manifolds (with R. Cleyton), J. Geom. Phys. 58 (2008), 1429-1449. math.DG/0702289.
• Nearly hypo structures and compact Nearly K\"ahler 6-manifolds with conical singularities (with M. Fernandez, V. Munos and L. Ugarte), J. London Math. Soc. 78 (2008), 580-604. math.DG/0602160.
• Conformal equivalence between certain geometries in dimension 6 and 7, (with R. Cleyton), Math. Res. Lett. 15 (2008), 631-641. math.DG/0607487.
• Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds, (with I. Minchev and S. Zamkovoy), to appear in "Handbook of pseudo-Riemannian Geometry and Supersymmetry" to be published by the European Mathematical Society EMS in the series IRMA Lectures in Mathematics and Theoretical Physics. math.DG/0511657.
• SU(3)-structures on submanifolds of a Spin(7)-manifold, (with F. Martin Cabrera), Diff. Geom. Appl. 26 (2008), 113-132. math.DG/0510406.
• On the geometry of closed $G_2$-structures, (with R. Cleyton), Commun. Math. Phys., 270 (2007), 53--67. math.DG/0306362.
• Locally conformal parallel $G_2$ and $Spin(7)$ manifolds, (with M. Parton and P. Piccinni), Math. Res. Lett., 13 (2006), 167--177. math.DG/0509038.
• Hyper-ParaHermitian manifolds with torsion, (with V. Tsanov and S. Zamkovoy), J. Geom. Phys. 56, (2006), 670-690. math.DG/0405585.
• Para-Hermitian and Para-Quaternionic manifolds, (with S. Zamkovoy), Diff. Geom. Appl. 23 (2005), 205-234. math.DG/0310415.
• $SU(3)$-instantons and $G_2, Spin(7)$ heterotic string solitons, (with P. Ivanov), Commun. Math. Phys. 259 (2005), 79-102. math.DG/0312094.
• Connection with torsion, parallel spinors and geometry of Spin(7) manifolds, Math. Res. Lett. 11 (2004), 171--186. math.DG/0111216.
• Quaternionic K\"ahler and hyperK\"ahler manifolds with torsion and twistor spaces, (with I. Minchev), J. reine angew. Math. 567 (2004), 215-233, math.DG/0112157.
• Deformations of generalized calibrations and compact non-Kahler manifolds with vanishing first Chern class, (with J. Gutowski and G. Papadopoulos), Asian J. Math. 7 (2003), 39-80, math.DG/0205012.
• Almost contact manifolds, connections with torsion, and parallel spinors, (with Th. Friedrich), J. reine angew. Math. 559 (2003), 217-236, math.DG/0111131.
• Killing spinor equations in dimension 7 and geometry of integrable $G_2$ manifolds, (with Th. Friedrich), J. Geom. Phys. 48 (2003), 1-11, math.DG/0112201
• Weyl structure with positive Ricci tensor, (with B. Alexandrov), Diff. Geom. Appl. 18 (2003), 343-350, math.DG/9902033.
• Parallel spinors and connections with skew-symmetric torsion in string theory, (with Th. Friedrich), Asian J. Math. 6 (2002), 303-336, math.DG/0102142.
• Geometry of Quaternionic Kaehler connections with torsion, J. Geom. Phys. 41 (2002), 235-257, math.DG/0003214.
• A no-go theorem for string warped compactification, (with G.Papadopoulos), Phys. Lett. B 497 (2001) 309-316, hep-th/0008232.
• Vanishing theorems and String Backgrounds, (with G.Papadopoulos), Class. Quantum Gravity 18 (2001), 1089-1110, math.DG/0010038.
• Harmonic spinors of Dirac operator of connection with torsion in dimension 4, (with P.Dalakov), Class. Quantum Gravity 18 (2001), 253-265, [PS]
• Vanishing theorems on Hermitian manifolds, (with B. Alexandrov), Diff. Geom. Appl. 14 (3) (2001), 251-265, math.DG/9901090.
• The Dolbeault operator on Hermitian spin surfaces, (with. B. Alexandrov and G. Grantcharov), Ann. Inst. Fourier (Grenoble) 51 1 (2001), 221-235, math.DG/9902005.
• Harmonic and holomorphic 1-forms on compact balanced Hermitian manifold (with G.Ganchev), Diff. Geom. Appl. 14 (1) (2001), 79-93. [PS]
• Holomorphic and Killing vector fields on compact balanced Hermitian manifolds, (with G.Ganchev), Int. J. Math. 11 (2000), 15-28. [PS]
• Dirac operators on Hermitian spin surfaces (with B. Alexandrov), Ann. Glob. Anal. Geom. 18 (2000), 529-539. [PS]
• Einstein-Weyl structures on certain compact conformal manifolds, Quart. J. Math. (Oxford) (2) 50 (1999), 457-462. [PS]
• Orthogonal complex structures on certain Riemannian 6-manifolds, (with V. Apostolov and G. Grantcharov), Diff. Geom. Appl. 11 (1999) 279-296. [PS]
• Riemannian manifold in which the skew-symmetric curvature operator has pointwise constant eigenvalues, (with I.Petrova), Geom. Dedicata 70 (1998), 269-282. [PS]
• Curvature properties of twistor spaces of quaternionic Kaehler manifolds, (with B. Alexandrov and G. Grantcharov), J. Geom. 62 (1998), 1-12. [PS]
• An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one form, (with B. Alexandrov and G. Grantcharov), J. Geom. Phys. 28 (1998), 263-270. [PS]
• Hermitian structures on twistor spaces, (with V. Apostolov and G. Grantcharov), Ann. Glob. Anal. Geom. 16 (1998), 291-308. [PS]
• Compact Hermitian surfaces of constant antiholomorphic sectional curvature, (with V.Apostolov and G.Ganchev), Proc. Amer. Math. Soc. 125 (1997), 3705-3714. [PS]
• Einstein-Hermitian surfaces and Hermitian Einstein-Weyl structures in dimension 4, (with P.Gauduchon), Mathematische Zeitschrift 226 (1997), 317-326. [PS]
• On the fundamental theorem for non-degenerate complex affine hypersurface immersions, Monatshefte Mathematics 123 (1997), 321-336. [PS]
• Riemannian manifolds in which certain curvature operator has constant eigenvalues along each circle, (with I.Petrova), Ann. Glob. Anal. Geom. 15 (1997), 157-171. [PS]

#### Препринти

• Formality of 7-dimensional 3-Sasakian manifolds, (with Marisa Fernandez and Vicente Munoz). arXiv:1511.08930.
• Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group, (with Ivan Minchev, Dimiter Vassilev). arXiv:1504.03142.
• Sasaki-like almost contact complex Riemannian manifolds, (with H. Manev and M. Manev). arXiv:1402.5426.
• Explicit Quaternionic Contact Structures and Metrics with Special Holonomy, (with L. C. de Andres, M. Fernandez, J. A. Santisteban, L. Ugarte and D. Vassilev), arXiv:0903.1398.
• Twistors of Almost Quaternionic Manifolds, (with I. Minchev and S. Zamkovoy), math.DG/0511525.
• Complex product structures on some simple Lie groups, (with V. Tsanov), math.DG/0405584.
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