Riemannian and pseudo-Riemannian geometry, spinor geometry, homogeneous spaces, transformation groups, differential geometry and PDEs, geometric structures on manifolds, holonomy groups and special geometry, generalized geometry, general relativity, Yang-Mills fields, supergravity, neurogeometry
Subject:
Differential Geometry and Lie Groups (Riemannian and pseudo-Riemannian geometry, homogeneous spaces, geometric structures) and their applications in mathematical physics, supergravity, neurogeometry
Biography
Leading Researcher (Institute for Information Transmission Problems of
the Russian Academy of Sciences - Kharkevich Institute). Member of Moscow Mathematical Society and Edinburgh Mathematical Society. Editor for "Differential Geometry and its Application", "Transformation groups", "International Journal of Geometric Methods in Modern Physics".
D. V. Alekseevsky, A. Santi, “Homogeneous symplectic $4$-manifolds and finite dimensional Lie algebras of symplectic vector fields on the symplectic $4$-space”, Mosc. Math. J., 20:2 (2020), 217–256
2009
2.
D. V. Alekseevsky, C. Medori, A. Tomassini, “Homogeneous para-Kähler Einstein manifolds”, Uspekhi Mat. Nauk, 64:1(385) (2009), 3–50; Russian Math. Surveys, 64:1 (2009), 1–43
3.
Dmitrii V. Alekseevskii, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 093, 16 pp.
1992
4.
D. V. Alekseevskii, M. M. Graev, “Twistors and $G$-structures”, Izv. RAN. Ser. Mat., 56:1 (1992), 3–37; Russian Acad. Sci. Izv. Math., 40:1 (1993), 1–31
5.
D. V. Alekseevskii, M. M. Graev, “Twistors of a Riemannian manifold, and CR-structures”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, 5, 3–19; Russian Math. (Iz. VUZ), 36:5 (1992), 1–16
1990
6.
D. V. Alekseevskii, “Contact homogeneous spaces”, Funktsional. Anal. i Prilozhen., 24:4 (1990), 74–75; Funct. Anal. Appl., 24:4 (1990), 324–325
1988
7.
D. V. Alekseevskii, “Maximally homogeneous $G$-structures and filtered Lie algebras”, Dokl. Akad. Nauk SSSR, 299:3 (1988), 521–525; Dokl. Math., 37:2 (1988), 381–384
8.
D. V. Alekseevskii, “Conformal mappings of $G$-structures”, Funktsional. Anal. i Prilozhen., 22:4 (1988), 68–69; Funct. Anal. Appl., 22:4 (1988), 311–313
9.
D. V. Alekseevskii, È. B. Vinberg, A. S. Solodovnikov, “Geometry of spaces of constant curvature”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 29 (1988), 5–146
10.
D. V. Alekseevskii, A. M. Vinogradov, V. V. Lychagin, “Basic ideas and concepts of differential geometry”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 28 (1988), 5–289
1987
11.
D. V. Alekseevskii, B. A. Putko, “Completeness of left-invariant metrics on Lie groups”, Funktsional. Anal. i Prilozhen., 21:3 (1987), 73–74; Funct. Anal. Appl., 21:3 (1987), 233–234
12.
D. V. Alekseevskii, A. M. Perelomov, “Kähler–Einstein metrics in holomorphic bundles”, Funktsional. Anal. i Prilozhen., 21:2 (1987), 66–67; Funct. Anal. Appl., 21:2 (1987), 144–146
1986
13.
D. V. Alekseevskii, A. M. Perelomov, “Invariant Kähler–Einstein metrics on compact homogeneous spaces”, Funktsional. Anal. i Prilozhen., 20:3 (1986), 1–16; Funct. Anal. Appl., 20:3 (1986), 171–182
1982
14.
D. V. Alekseevskii, “Lie groups”, Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 20 (1982), 153–192; J. Soviet Math., 28:6 (1985), 924–949
1979
15.
D. V. Alekseevskii, “On perfect actions of Lie groups”, Uspekhi Mat. Nauk, 34:1(205) (1979), 219–220; Russian Math. Surveys, 34:1 (1979), 215–216
1978
16.
D. V. Alekseevskii, B. N. Kimel'fel'd, “Classification of homogeneous conformally flat Riemannian manifolds”, Mat. Zametki, 24:1 (1978), 103–110; Math. Notes, 24:1 (1978), 559–562
1975
17.
D. V. Alekseevskii, B. N. Kimel'fel'd, “Structure of homogeneous Riemann spaces with zero Ricci curvature”, Funktsional. Anal. i Prilozhen., 9:2 (1975), 5–11; Funct. Anal. Appl., 9:2 (1975), 97–102
18.
D. V. Alekseevskii, “Classification of quaternionic spaces with a transitive solvable group of motions”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 315–362; Math. USSR-Izv., 9:2 (1975), 297–339
19.
D. V. Alekseevskii, “Homogeneous Riemannian spaces of negative curvature”, Mat. Sb. (N.S.), 96(138):1 (1975), 93–117; Math. USSR-Sb., 25:1 (1975), 87–109
1974
20.
D. V. Alekseevskii, “Lie groups and homogeneous spaces”, Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 11 (1974), 37–123; J. Soviet Math., 4:5 (1975), 483–539
1973
21.
D. V. Alekseevskii, “$S^n$ and $E^n$ are the only Riemannian spaces that admit an essential conformal transformation”, Uspekhi Mat. Nauk, 28:5(173) (1973), 225–226
1972
22.
D. V. Alekseevskii, “Groups of conformal transformations of Riemannian spaces”, Mat. Sb. (N.S.), 89(131):2(10) (1972), 280–296; Math. USSR-Sb., 18:2 (1972), 285–301
1971
23.
D. V. Alekseevskii, “Conjugacy of polar factorizations of Lie groups”, Mat. Sb. (N.S.), 84(126):1 (1971), 14–26; Math. USSR-Sb., 13:1 (1971), 12–24
1970
24.
D. V. Alekseevskii, “Quaternion Riemann spaces with transitive reductive or solvable groups of motions”, Funktsional. Anal. i Prilozhen., 4:4 (1970), 68–69; Funct. Anal. Appl., 4:4 (1970), 321–322
1968
25.
D. V. Alekseevskii, “Compact quaternion spaces”, Funktsional. Anal. i Prilozhen., 2:2 (1968), 11–20; Funct. Anal. Appl., 2:2 (1968), 106–114
26.
D. V. Alekseevskii, “Riemannian spaces with exceptional holonomy groups”, Funktsional. Anal. i Prilozhen., 2:2 (1968), 1–10; Funct. Anal. Appl., 2:2 (1968), 97–105
2013
27.
D. V. Alekseevskii, A. S. Galaev, S. V. Galaev, A. V. Gokhman, “In memory of Losik Mark Vol'fovich”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:4(1) (2013), 118–122
1997
28.
D. V. Alekseevskii, V. O. Bugaenko, G. I. Olshanskii, V. L. Popov, O. V. Schwarzman, “Érnest Borisovich Vinberg (on his 60th birthday)”, Uspekhi Mat. Nauk, 52:6(318) (1997), 193–200; Russian Math. Surveys, 52:6 (1997), 1335–1343
Introduction to neurogeometry of vision D. V. Alekseevsky General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences March 12, 2015 14:00
11.
Нейрогеометрия зрения D. V. Alekseevskii Dynamical systems and statistical physics March 4, 2015 18:30
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