symmetric and semi-symmetric spaces,
Einstein and semi-Einstein spaces,
Ricci-semi-symmetric spaces and submanifolds,
submanifolds with parallel and semi-parallel tensor fields,
Einstein submanifolds,
semi-Einstein submanifolds.
The general classification theorem for Riemannian Ricci-semi-symetric (Ricci-semi-parallel) spaces was proved; were introduced semi-Einsteinian spaces and was showed that an arbitrary cone over Einsteinian space is a semi-Einsteinian space; the local classification and geometric description of some classes of the Ricci-semi-parallel submanifolds (in particular the hypersurfaces) in Euclidean spaces was given. The fundamental problem on a connection between the submanifolds with the parallel tensor fields and the submanifolds with semiparallel tensor fields was solved in the spaces of constant curvature. The number of papers was devoted to the submanifolds with parallel higher order fundamental forms, semiparallel submanifolds and submanifolds with the parallel Ricci tensor.
Biography
Graduated from Faculty of Mathematics and Mechanics of Yerevan State University in 1972 (department of algebra and geometry). Ph.D. thesis was defended in 1980. D.Sci. thesis was defended in 1999. A list of my works contains 70 titles.
Main publications:
Mirzoyan V. A. Ric-poluparallelnye podmnogoobraziya // Itogi nauki i tekhn. Problemy geometrii, 1991, 23, 29–66.
Mirzoyan V. A. Strukturnye teoremy dlya rimanovykh Ric-polusimmetricheskikh prostranstv // Izv. Vuzov. Matematika, 1992, 6, 80–89.
Mirzoyan V. A. Obobscheniya teoremy Yu. Lumiste o poluparallelnykh podmnogoobraziyakh // Izv. NAN Armenii. Matematika, 1998, 33(1), 53–64.
Mirzoyan V. A. Klassifikatsiya Ric-poluparallelnykh giperpoverkhnostei v evklidovykh prostranstvakh // Matem. sbornik, 2000, 191(9), 65–80.
V. A. Mirzoyan, “Normally flat semi-Einstein submanifolds of Euclidean spaces”, Izv. RAN. Ser. Mat., 75:6 (2011), 47–78; Izv. Math., 75:6 (2011), 1135–1164
2008
3.
V. A. Mirzoyan, “Classification of a class of minimal
semi-Einstein submanifolds with an integrable conullity distribution”, Mat. Sb., 199:3 (2008), 69–94; Sb. Math., 199:3 (2008), 385–409
V. A. Mirzoyan, “Structure theorems for Ricci-semisymmetric submanifolds
and geometric description of a class of minimal semi-Einstein
submanifolds”, Mat. Sb., 197:7 (2006), 47–76; Sb. Math., 197:7 (2006), 997–1024
V. A. Mirzoyan, “Warped products, cones over Einstein spaces, and classification of Ric-semiparallel submanifolds of a certain class”, Izv. RAN. Ser. Mat., 67:5 (2003), 107–124; Izv. Math., 67:5 (2003), 955–973
V. A. Mirzoyan, “Classification of Ric-semiparallel hypersurfaces in Euclidean spaces”, Mat. Sb., 191:9 (2000), 65–80; Sb. Math., 191:9 (2000), 1323–1338
V. A. Mirzoyan, “Submanifolds with higher-order semiparallel fundamental forms as envelopes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 8, 79–80; Russian Math. (Iz. VUZ), 42:8 (1998), 75–76
V. A. Mirzoyan, “On a class of submanifolds with a parallel fundamental form of higher order”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 6, 46–53; Russian Math. (Iz. VUZ), 42:6 (1998), 42–48
V. A. Mirzoyan, “Submanifolds with symmetric fundamental forms of higher orders as envelopes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1997, no. 9, 35–40; Russian Math. (Iz. VUZ), 41:9 (1997), 33–37
V. A. Mirzoyan, “Semisymmetric submanifolds and their decompositions into a product”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 9, 29–38; Soviet Math. (Iz. VUZ), 35:9 (1991), 28–36
V. A. Mirzoyan, “Decomposition into a product of submanifolds with the parallel fundamental form $\alpha_s$ ($s\ge3$)”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 8, 44–54; Soviet Math. (Iz. VUZ), 35:8 (1991), 42–51
V. A. Mirzoyan, “Submanifolds with a commuting normal vector field”, Itogi Nauki i Tekhniki. Ser. Probl. Geom., 14 (1983), 73–100; J. Soviet Math., 28:2 (1985), 192–207
Contact us: