# Dmitri Alekseevsky

Dmitri Alekseevsky | |
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Дмитрий Владимирович Алексеевский | |

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Born | Dmitri Vladimirovich Alekseevsky August 20, 1940 Moscow, Russian RSFR, Soviet Union |

Nationality | Russian |

Citizenship | Russia |

Education | Ph.D. in Geometry and Topology |

Alma mater | Moscow State University |

Occupation | Mathematician |

Known for | Alekseevsky's conjecture, Alekseevskian spaces |

Awards | Leverhulme Emeritus Fellowship |

**Dmitri Vladimirovich Alekseevsky** (Дмитрий Владимирович Алексеевский) (born August 20, 1940 in Moscow) is a Russian mathematician. He is known worldwide for his outstanding contributions in differential geometry and especially in Lie theory, with interest for different research fields ranging from mathematical physics to neurogeometry.

## Contents

## Life and career

Dmitri Alekseevsky studied mathematics at the Moscow State University where he received his Ph.D. in Geometry and Topology at 1967 under the supervision of Ernest Vinberg.^{[1]}
From 1967 till 1976 he was a researcher at the Research Institute of Semi-Products in Moscow, and in the period 1976-1987 he was a senior lecturer at the Moscow State Pedagogical University.
In 1989 he received Sc.D. in Mathematics (equivalent to the German Habilitation) from the Institute of Mathematics in Novosibirsk (Siberia Branch of Academy of Science) with specialization in geometry and topology. For 3 years he was an associate professor at the Moscow State Pedagogical University.

Between 1990 and 2000, Alekseevsky led research teams as a Chief researcher at the Scientific Center "Sophus Lie" in Moscow. For two years he was a visiting professor in Max-Planck Institute in Bonn (during 1995-1996, 1998-1999, and the spring semester of 2000), while in the period 1996-1997 he was a visiting professor in the Erwin Schrödinger Institute (ESI) in Vienna.
In 2000 he was appointed professor at the University of Hull in the School of Mathematics & Physical Sciences where he had a chair of pure mathematics till 2005. Since 2005, Alekseevsky is an Emeritus Professor at the University of Hull, where he was awarded the Leverhulme Emeritus Fellowship^{[2]}^{[3]}. The period 2006-2009 he was a visiting professor in Edinburgh University, while from 2009 to 2012 he was a Honorable Fellow in the same university. The decade 1995-2005 Alekseevsky was the organiser of a series of conferences and workshops related to holonomy theory, special geometric structures, superalgebras in string theory, and other topics.

From 2011, Alekseevsky has been a leading researcher in the Russian Academy of Sciences, at the Institute of Information Transmission Problems in Moscow. The period 2011-2014 he was a visiting professor in Masaryk University (Faculty of Science, Department of Mathematics Statistics), while from 2014 he has been a visiting professor in University of Hradec Králové, Faculty of Science.

Dmitri Alekseevsky has been an editor of the following journals: "Differential Geometry and its Applications" (since 1989), "Transformation groups" (since 1995), "Annals of Global Analysis and Geometry" (since 2001), "International J. of Geom. Methods in Modern Phys." (since 2003), and "Monatshefte für Mathematik" (since 2004). The period 1978-1987 he was a reviewer for the Soviet Physical Reviews, while since 1987 he is a reviewer for Zentralblatt Math. Alekseevsky is a member of the Edinburgh Mathematical Society.

## Mathematical work

Alekseevsky has more than 130 original articles reviewed in MathSciNet, with impact on the literature of both mathematics and theoretical physics^{[4]}. He is particularly renowned for his contributions to holonomy theory and the theory of quaternionic structures, homogeneous Ricci-flat manifolds, homogeneous Kähler-Einstein manifolds ^{[5]}, cohomogeneity-one manifolds^{[6]}, the Alekseevsky's conjecture^{[7]}, and other central concepts in modern differential geometry. He constructed the first examples of quaternionic Kähler manifolds that were not locally symmetric and classified homogeneous quaternionic Kähler manifolds with a simply transitive completely solvable group of isometries, know as *Alekseevskian spaces*^{[8]}.

### Books

- Alekseevsky, D. V.; Vinogradov, A. M.; Lychagin, V. V. (1991),
*Geometry I. Basic Ideas and Concepts of Differential Geometry*, Encyclopedia of Mathematical Sciences,**28**, Berlin Heidelberg: Springer-Verlag, ISBN 978-3-540-51999-7. Translated from the 1988 original Russian edition by E. Primrose.^{[9]} - Alekseevsky, D. V.; Vinberg, E. B.; Solodovnikov, A. S. (1993),
*Geometry II. Geometry of spaces of constant curvature*, Encyclopedia of Mathematical Sciences,**29**, Berlin Heidelberg: Springer-Verlag, pp. 1–138, doi:10.1007/978-3-662-02901-5_1, ISBN 978-3-540-52000-9, MR 1254932. Translated from the original Russian edition by V. Minachin.

Dmitri Alekseevsky has translated to Russian the following books:

*Lectures on Differential Geometry*of Shlomo Sternberg, Chelsea Publ. Co., New York, 1983. First edition: Prentice Hall, Inc. Englewood Cliffs, N.J., 1964, (Russian Translation)*Лекции по Дифференциальной геометрии*, Mir, Moscow (1970).*Einstein manifolds, Vol I, II*of Arthur Besse with a preface. (Russian Translation)*Многообразия Эйнштейна*, Том I,II, "Mir", Moscow, 1990. Vol. I: 320 pp.; Vol. II: pp. 321–704.

## In the media

## References

- ↑ Dmitri Alekseevsky in Mathematics Genealogy Project
- ↑ https://www.leverhulme.ac.uk/emeritus-fellowships
- ↑
*Dmitri Alekseevsky - Emeritus Fellowships*(PDF), October 2005, (page 22) by the*Newsletter*of the London Mathematical Society - ↑ Bourguignon, Jean-Pierre (2006), "Some Highlights of Dmitry Alekseevsky's Work",
*International Journal of Geometric Methods in Modern Physics*,**03**(5n06): 823–831, Bibcode:2006IJGMM..03..823B, doi:10.1142/S0219887806001636, by Jean-Pierre Bourguignon - ↑
*Dmitri Alekseevsky - Flag manifolds*(PDF) - ↑
*On the geometry of cohomogeneity-one manifolds with positive curvature*(PDF), by W. Ziller - ↑ Böhm, Christoph; Lafuente, Ramiro A. (2018),
*Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds*, arXiv:1811.12594, by C. Böhm and R. Lafuente - ↑
*Alekseevskian spaces*(PDF), by V. Cortés - ↑ Mathscinet for the Russian edition of
*Geometry I. Basic Ideas and Concepts of Differential Geometry*[1]

## External links

- Dmitri Alekseevsky
- D. Alekseevsky - Publications
- Dmitri ALEKSEEVSKY | Leading Researcher, Emeritus
- Dmitri Alekseevsky | University of Edinburgh - Academia.edu
- SOME HIGHLIGHTS OF DMITRY ALEKSEEVSKY'S WORK
- Dmitry Vladimirovich Alekseevsky in nLab
- Dmitri Alekseevsky - Geometry of Differential Equations

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