List of Publications (before 2000)

 

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MONOGRAPHS AND SURVEY ARTICLES

 

1.

Lie groups and homogeneous spaces, VINITI Publ. Algebra, Topol., Geom., 1974,v.11,31-126.

2.

Lie groups, VINITI Publ., Algebra, Topol., Geom.,  1982, v.20, 153-178.

3.

Geometry I (Basic Ideas and Concepts of Differential Geometry), Encycl. of Math. Sciences, v.28, 264p., Springer-Verlag, 1991 (with A.M.Vinogradov and V.V.Lychagin )

4.

Geometry 2 (Geometry of spaces of constant curvature), Encycl. of Math. Sci., v.29, 1-146, 1993, Springer Verlag (with E. B. Vinberg and A. S. Solodovnikov)

5.

 Differential Geometry of curves and surfaces, Center "Sophus Lie", 1991 (in Russian).

 

 

ARTICLES FOR ENCYCLOPAEDIA OF MATHEMATICS

  (Russian edition, VINITI, v.1-5, 1978-1984 )

 (English edition, Kluver publ.,1988-1994 )

 

6.

 Differential Geometry of Manifolds,v.2,1979,254-260.

7.

Invariant Objects on Homogeneous Space,v,2,538-540.

8.

Quaternionic Structure,v.2,839-840.

9.

Conformal Structure,v.2,1089-1090.

10.

Lie derivative,v.3,1982,260-261.

11.

 Lie differential,v.3,1982,261.

12.

 Noeter's theorems,v.3,261-263.

13.

Homogeneous space,v.3,1175-1179.

14.

 Parallelizable manifold,v.4,1984,204-205.

15.

Almost complex structure,v.4,541-542.

16.

Almost symplectic structure,v.4, 548-549.

17.

Reducible Riemannian spaces,v.4,633.

18.

Pseudo-group structure,v.4,732-734.

19.

Pfaff problem,v.4,773-774.

20.

 Pfaff structure, v.4.774-775.

21.

Homogeneous Riemannian space,v.4,1026-28.

22.

 Homogeneous symplectic space,v4,1157-1159.

23.

Absolute parallelizability ,v.4,204-205.

24.

Parallel field, v.4, 208-209.

25.

Group of transformations 1-parameter,1170-71

26.

Chart, v.2, 729-730.

27.

Invariant metric, v.2, 529-531.

28.

Spinor structure,v.5,1984,139-141.

29.

Structure, v.5, 249-250.

30.

G-structure,v.5,250-253.

31.

Flag, v.5, 628.

32.

Flag structure,v.5,628-629.

33.

Hermitian metric,v.5,1019-1020.

34.

Hermitian structure, v.5, 1020-1021.

35.

Yang-Mills field,v.5,1059-1060.

36.

 Lie algebra,in  Physics Encyclopedia (in Russian), 1988,Sov.Encycl.

37.

Symmetric space,Physics Encyclopedia (in Russian), 1988, Sov.Encycl.

 

 

  PAPERS

 

38.

 On holonomy group of Riemannien  spaces,  Ukr.Mat.J., 1967, 19, 100-104.

39.

Riemannian spaces with non-standard holonomy groups, Funct. Anal. & its Applications, 1968, 2, 1-10.

40.

 Compact quaternionic spaces, Funct. Anal.Appl.,1968,v.2,11-20.

41.

Quaternionic Riemannian spaces with transitive reductive or solvable group of motions, Funct.Anal. Applic.,1970,4,n4,68-69.

42.

Conjugation  of the polar decompositions  of  Lie  groups, Mat.Sb.,1971, v.84, n1,14-26.

43.

Groups of  conformal  transformations of Riemannian spaces,Mat.Sb.,1972, v.89, n1, 280-296.

44.

 Holonomy  groups in General Relativity, Proc.Sov.Gravit. Confer., Erevan, 1972,3-6.

45.

The sphere and the Euclidean space are the only Riemannian manifolds with essential conformal transformations, Uspekhi Mat. Nauk, 1973, 28, n5, 289-290.

46.

Holonomy groups and recurrent  tensor  fields  in Lorentzian  manifolds,  Probl. Gravit. Theory and Elem. Part., 1974, n5, 5-17.

47.

Homogeneous Riemannian spaces of negative curvature, Mat.Sb., 1975, 96,n1,93-117.

48.

Classification of quaternionic spaces with   transitive solvable groups of motions, Math USSR Izv., 1975, 39, n2, 315-362.

49.

Homogeneous Riemannian manifolds with zero Ricci curvature, Funct. Anal. and its Applic., 1975, v 2, 5-11(with B.N.Kimelfeld)

50.

Riemannian metrics consistent with G-structure, Proc. Confer. "150 anniversary of Lobachevsky Geometry",1976,9.

51.

 Selfsimilar spaces, holonomy groups and invariants of a linear representation of the line, Proc. Confer. "150 anniversary of Lobachevsky Geometry", 1976, 8.

52.

Classification of homogeneous conformally flat  Riemannian manifolds, Mat. Zam., 1978, 24, n1,103-110 (with B. N. Kimelfeld).

53.

 On proper  actions of Lie groups, Uspekhi Mat. Nauk, 1978, 34, n1, 219-220.

54.

 Examples of  simple infinite-dimensional Lie superalgebras of vector fields, Proc. Bulg. Acad. Sci., 1980, v.33, n4, 1189-1190 (with D. A. Leites and I. M. Schepochkina ).

55.

 Self-similar Lorentzian  manifolds,  Ann. Glob. Anal. and Geom., 1985, 3, 59-84.

56.

 Invariant K\"ahler-Einstein  metrics  on  compact   homogeneous spaces, Funct. Anal. Applic., 1986, 20, n3, 1-16 (with A. M. Perelomov).

57.

Homogeneous Einstein metrics, Diff.Geom.and its Appic. Brno,1987,1-21.

58.

On the completeness of left-invariant metric on Lie  group, Funct. Anal. Applic. 1987, 21, n3, 73-74 (with B. A. Putko ).

59.

K\"ahler-Einstein metrics on holomorphic vector bundles, Funct. Anal. Applic.,1987, 21, n2, 66-67 (with A. M. Perelomov).

60.

On the length of minimal geodesics in quaternionic manifolds, Proc. All-Union Conf. on Geometry in the Large,  1987, Novosibirsk,4.

61.

 Maximally homogeneous G-structures and filtered Lie algebras, Sov. Math. Dokl., 1988, n3, 521-525.

62.

 Calabi-Yau metric on Fermat manifold, J. Geom.  and Phys., 1989, n4, (with M. M. Graev )

63.

The completeness  of left-invariant Lorentzian metrics on Lie groups,  Topol. and geom. methods in  analysis, 1989, Voronez Univ., 12-28 (with B. A. Putko), Lect. Notes Math., n.1453, 1990, 171-186

64.

Homogeneous contact manifolds, Funct.Anal. applic., 1990,n4.

65.

Riemannian manifolds of cohomogeneity one, Proc. Colloq. on Diff. Geom. Eger, 1991, 1-19.

66.

G-manifolds with one-dimensional orbit space, Adv. in Sov. Math., 1992, v.8, 1-31, (with A. V. Alekseevsky )

67.

Riemannian manifolds with one-dimensional orbit space, Preprint of Roma University,1991, 32p.,(with A. V. Alekseevsky), Ann. of Glob. Anal.,1993, v.11, 197-211.

68.

Twistors and G-structures, Math. USSR Isv.,1992, n1, (with M.M.Graev)

69.

 G-structures of twistor type and their twistor spaces, Preprint of Roma University,32p.,1991 (with M.M.Graev), J. of Geom. and Phys., 1993, v.10,203-229.

70.

 Space-homogeneous Lorentzian manifolds, Tartu Univ. Toimetised, 1992, v.940, 17-20.

71.

 CR structures and twistor spaces,Izvestia VUZ,1992, v.5. 323-331, (with M.Graev)

72.

Characteristic classes for G-structures (with P.Michor), Differ. Geom. and Applic.,1993,v.3, n 4,323-331.

73.

Quaternionic-like structures  on a manifold. 1-integrability and integrability  conditions  (with S.Marchiafava   ),  Rendiconti della Accad. Lincei, 1993,v.4,s.9,43-52.

74.

Quaternionic-like structures on a manifold.Automorphism groups and their interrelations (with S.Marchiafava ), Rendiconti della Accad. Lincei, 1993, v.4,s.9,53-61.

75.

 Asystatic G-manifolds (with A.V.Alekseevsky), Preprint ESI, 1993, n 21, 21p., Proceed. of the Workshop on Diff. Geom. and Topol., Ed. R.Caddeo and F.Tricerri, 1993, 1-22.

76.

Differential geometry of g-manifolds.I. g-manifolds of  constant rank and their characteristic classes (with P.Michor ), Preprint ESI, 1993, n39, 23p.,  Diff. Geom. Applic.,1993, v.3, 323-329.

77.

 Differential geometry of Cartan connections (with P.Michor), Preprint ESI, 1993, n39, 23p., Publ. Math. Debrecen, 1995, v.47, n3-4, 349-375.

78.

Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions (with J.Grabovski, G.Marmo,P.Michor ),Preprint ESI 1993, 20p., J. Math. Phys., 1994,v.35,n5, 4909-4927.

79.

 Poisson brackets on simple Lie algebras and symplectic  Lie algebras (with A.Perelomov ),Preprint CERN-TH.6984/93,37p.

80.

 Generalized reductive homogeneous spaces and quasi-graded semisimple Lie algebras (with Spiro),Preprint of University of Ancona ,1993,22p,  Proceed. Intern. Conference "Algebra and Analysis", Kasan 1996,1-22, ed. Arlasanov, Parshin, Schafarevich.

81.

Homogeneous Ricci-positive 5-manifolds (with I. Dotti-Miatello, C. Ferraris), Preprint Univ. of  Cordoba, 1993, n28, 11p.; Pacific Math. J., v. 175, n 1, 1-12, 1996

82.

Grassman and HyperKaehler structures on some spaces of sections of holomorphic bundles (with M.Graev), Preprint IHES M/94/31 17p.; in "Manifolds and Geometry", Symposium Math.,v. 36, ed. P. de Bartolomeis, F.Tricerri, E.Vesentini, 1-19, 1996

83.

Canonical metric on a quaternionic manifold (with S.Marchiafava ),Proceed. Conf. on Geom. and Topol., Timisoara, 1994, 8p.

84.

Gradient quaternionic vector fields and  characterization of the quaternionic projective space (with S.Marchiafava), Preprint ESI, 1994, n138, 8p.

85.

Quaternionic transformations and the first eigenvalue of the Laplacian (with S.Marchiafava ), Preprint ESI, 1994, n150, 15 p.

86.

Transformations of quaternionic K\"ahler  manifolds  (with S.Marchiafava)  Compt. Rend, 1995, 320,n 6,703-708

87.

Almost quaternionic Hermitian and quasi-Hermitian manifolds   (with S. Marchiafava) in "Almost complex structures", ed. Sekigava, Dmitriev, WorldScientific. 1995, 150-176

88.

Hypercomplex structures on quaternionic manifolds (with S.  Marchiafava) in " New developments in differential geometry"  ed. L.Tomassy, J.Szenthe Kluver publ., Dodrecht, Boston, London, 1996, 1-20

89.

On some structure equations for almost quaternionic Hermitian   manifolds ( with E.Bonan, S.Marchiafava) in "Complex   structures and vector fields", 1995, 114-135

90.

 Quaternionic structures on a manifold and subordinated  structures (with S.Marchiafava), Ann. Matem. pura ed appl.,  1996, 1-69, v.171, n 4

91.

 Quaternionic transformations of a non-positive quaternionic   K\"ahler manifold (with S.Marchiafava) ,Preprint MPI 95-126,   Intern. J. of Math., v.8,No 3, 1997, 301-316

92.

Differential geometry of $\frak G$-manifolds (with P.Michor)  Diff. Geom. and  Applic., 1995, 5, 371-403

93.

 Mirror Supersymmetry in the space of (super)extended Poincare  algebras $\frak p (p, q) $ (with V.Cortes), Lettr. in Math. Phys., 1996 , 38,283-287

94.

Homogeneous quaternionic K\"ahler manifolds of unimodular  group (with V.Cortes) Preprint MPI/95-95,12 p.,   Boll. Union.  Math. Italiano, v.11B, suppl. fasc.2, 1997,217-229

95.

 Classification of N-(super)extended Poincare algebras and  bilinear invariants of the spinor representation of   spin(p, q) (with V.Cortes), Preprint MSRI 088-95,   Commun. Math. Phys.,v. 183,1997, 477-510

96.

 Isometry groups of homogeneous quaternionic K\"ahler manifolds   (with V.Cortes), Preprint ESI 230, 1995, 39 p. J.  of Geom. Anal. v.9, n 4, 513-545 , 1999

97.

 Choosing of roots of polynomial smoothly (with A.Kriegl, M.Losik, P.Michor), Preprint ESI, 314, 1996, 20 p.,  Israel J. Math., 105, 1998, 203-233

98.

 Poisson and symplectic structures on Lie algebras.  1,(with   A.M.Perelomov), Preprint MPI 96-33, 25p., J. of Math. and Geom., 22, 1997,191-211

99.

On decomposibility of Nambu-Poisson tensor (with P.Guha),  Preprint MPI, 96-9, 9p.; Acta Math. Univ.Comenianae,v. 65, 1-9, 1996

100.

Killing spinors are Killing vector fields in Riemannian supergeometry ( with V.Cortes, C. Devchand, U. Semmelmann ) preprint MPI 97-29, 15 p., J. of Geom.  and Phys.,v.26, n.1-2, 35-50, 1998

101.

 Flag manifolds , Preprint ESI, n 415,1997,32 p.; Zbornik Radova,book 6 (14), 11 Yugoslav. Seminar,1997, Beograd, 3-35

102.

 Isotropy representation of flag manifolds, in Proceed. 17 Winter Srni School, ed. J. Slovak et al.,Suppl.  Rendic. di Circ. Matem. di Palermo, 13-24 , 1998

103.

Compatible complex structures on almost quaternionic manifold ( with S. Marchiafava and M.Pontecorvo ), Preprint ESI n 404,18p.;  Trans. Amer. Math. Soc.,v 351,n 3,1999, 997-1014

104.

Compatible  complex structures on a quaternionic K\"ahler manifold, (with S. Marchiafava, M. Pontecorvo) Preprint ESI n 419, 33 p.; Ann. Glob. Anal. and Geom., v 16, 419-444, 1998

105.

Completely integrable systems: A generalization, Preprint ESI n 452, 1997, 15, Modern Physics Letters, A v.12, 1637-1648, 1997

106.

Cohomogeneity one manifolds of positive characteristic and quaternionic K\"ahler manifolds (with F.Podesta), Preprint ESI n 466 , 1997, 32 p.; Geometry, Topology and Physics, Procedings of the first Brasilian-USA workshop in Campinas, ed. B.Apanasov, S.Bradlov,  W.Rodrigues, K.Uhlenbeck 1998

107.

Poisson structures on double Lie groups ( with J.Grabovski, G.Marmo, P.W.Michor ), Preprint ESI ,n 465,1997,37p., J. of Geom.and   Phys. v 26, 340-379, 1998

108.

 Some geometric aspects of compatible complex structures on a quaternion  K\"ahler  manifold ( with S. Marchiafava, M.Pontecorvo), Proceed. 18 Srni Winter School "Geometry andPhysics",  in Suppl. Rendic. di Circ. Matem. di Palermo, 1999

109.

Self-duality and pointwise Osserman manifolds (with N.Bla\u{z}i\'c, N.Bokan, Z.Raki\'c), Arch. Math., (Brno), 1999, no. 3, 193-201

110.

Almost complex submanifolds of a quaternionic K\"ahler manifold (with S. Marchiafava), Proceed. of Brasov conference in Differential Geometry, 1999, 1-8