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  • .

    2017

  • 2005,

    ( 2006).

    () -

    *

  • 1 1

    1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.5 . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.6 . . . . . . . . . . . . . . . . . . . . . . . 2

    1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.9 . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    2 4

    2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.5 . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.6 . . . . . . . . . . . . . . . . . . . . . . . 9

    2.7 . . . . . . . . . . . . . . . . . . . . . . . 10

    2.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.9 . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.10 . . . . . . . . . . . . . . . . . . . . . 12

    3 13

    3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    3.2 . . . . . . . . . . . . 13

    3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    3.5 . . . . . . . . . . . . . . . . . . . . . . . 16

    3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    4 17

    5 23

    5.1 . . . . . . . . . . . . . . . . . . . . . . . . . 23

    5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

    5.5 . . . . . . . . . . . . . . . . . 67

    i

  • 1.

    1.1.

    : 9 1945, .

    : . .

    : 24, 164 51. . 210-9941927

    : evassil@math.uoa.gr

    URL: http://users.uoa.gr/ evassil

    Research Gate: Efstathios Vassiliou

    : , -

    () ( 2011).

    * : -

    . , 20067

    Chern-

    Weil" .

    1.2.

    ( , 1979)

    ( , 1973)

    ( , 1968).

    1.3.

    1976 () -

    ( 103, . /27-2-76)

    1979 ( 1979)

    ( 145, . ..../8-8-79)

    1979 ( 241, . ..../11-12-79)

    1982 , . 1268/1982 ( 187,

    . ..../26-8-82)

    1984 ( )

    ( 23, . ..../14-2-84)

    1987 ( 92, . ..../6-6-88)

    2011 .

    1

    http://users.uoa.gr/~evassilhttps://www.researchgate.net/profile/Efstathios_Vassiliou

  • 1.4.

    . ,

    ( Banach, Frechet) Lie,

    ( Lie), (

    ). -

    Mathematical Reviews: 18B40, 18F15, 18F20, 53C05, 53C30, 55N30, 57R22,

    58A20, 58A30, 58B10, 58B20, 58B25.

    1.5.

    ( )

    1963 , 18 & 6/11.

    .

    1968 , 7 & 10/12.

    1967, -

    , . . ,

    . -

    1973 .

    ( 1974 - -

    1975), 1976 -

    , 2011.

    1.6.

    1972-73

    Leeds .

    (. G. R. Allan), (A. West

    S. Carter) (E. Stout).

    - 1976 -

    1977 , Guest Staff Member,

    Aarhus . -

    : (J. Dupont),

    (Singularities) (H. A. Salomonsen)

    ( J. Dupont I. Madsen).

    1979 - 1980 ,

    , . -

    P. Libermann ( Paris VII),

    Lie A. Lichnerowicz ( College de Fra-

    nce) - , Pham Mau

    Quan G. Pichon ( Poincare).

    1991-92 ,

    , Cambridge () Visiting Scholar.

    2

  • 1.7.

    1. Corso Estivo di Matematica,

    (CNRS) Scuola Normale Superiore ( 1971).

    2. Representations of Lie Groups and Harmonic Analysis,

    ( 1977).

    3. Summer Seminar on Complex Analysis, (ICTP)

    ( 1980).

    4. Summer Workshop on Fibre Bundles and Geometry, ( 1982).

    1.8.

    1. .., (1963-1967).

    2. (British Counsil), -

    Leeds.

    3. , -

    Aarhus.

    4. 4 ,

    1.7,

    .

    1.9.

    :

    American Mathematical Society,

    London Mathematical Society,

    Societe Mathematique de France,

    Balkan Society of Geometers.

    , , (..).

    1.10.

    , , .

    3

  • 2.

    2.1.

    :

    : (Affine) , , -

    , (

    Lie), ( Riemann

    ), - ( ).

    : ( ), -

    .

    2.2.

    ,

    , , ,

    :

    1976-77 ( ): Gauss Hopf-Rinow. -

    D. Gromoll W. Klingen-

    berg W. Meyer: Riemannsche Geometrie im Grossen, Lecture Notes in Mathematics

    #55, Springer ( . ).

    1980-81 (): Lie-Banach. Lie-

    Banach N.Bourbaki: Groupes et Algebres de Lie, Chapitres 23

    J. Marsden: Hamiltonian Mechanics, Infinite Dimensional Lie

    Groups, Geodesics Flows and Hydrodynamics (Berkley, 1968).

    1981-82 (): .

    , -

    N. Bourbaki: Varietes Differentielles et

    Analytiques (fascicule de resultats, 17) S. Lang: Introduction to

    Differentiable Manifolds.

    1981-82 ( ): . -

    W. Drechsler M. E. Mayer: Fibre Bundle Techniques

    in Gauge Theories, Lecture Notes in Physics #67, Springer, D. Bleecker: Gauge

    Theory and Variational Principles. 4 -

    .

    1983-84 (): . -

    ( ) S. G. Kren

    N. Jackin, [.

    3.6 ( # 2)].

    1984-85 ( ): Floquet-Liapunov.

    Floquet-Liapunov

    ( )

    4

  • , -

    (. ). ,

    , .

    1987-88 ( ): .

    (-

    ) , .

    1988-89 (): .

    -

    .

    1992-93 (): Lie.

    K. Mackenzie: Lie Groupoids and Lie Algebroids in Dif-

    ferential Geometry, LMS Lecture Notes Series 124 (1987).

    (

    ) . .

    1994-95 (): Banach Frechet.

    ( J. A. Leslie, H. Omori, M. E. Verona),

    Banach Lie-Banach.

    ( ) . -

    ,

    .

    1996-97 ( ): Sikorski. -

    . . .

    , R.

    Sikorski , -

    . (

    ) . .

    1997-98 ( ): LaTEX AMS-LaTEX .

    -

    .

    2000-01 (): . . -

    . -

    . . (. Geometry of Vector Sheaves,

    Vols. I-II, Kluwer, 1999), -

    .

    .

    2001-02 ( ): . -

    . . ,

    J. Leslie Frechet,

    P. Michor A. Kriegl,

    The convenient setting for global Analysis, AMS, 1997.

    5

  • 2002-03 ( ): . -

    , . , .

    , . , . , . . .

    2007-08 ( ): * . , - Kobayashi ( . ),

    ( . -

    ), A- ( . -

    ).

    2008-09 ( ): * . Chern-Weil ( . ).

    -

    , :

    1. N. Karkanias (The City University, ):

    ( 1983).

    2. A. Asada (Shinshu University, ): Non-abelian de Rham Theory (

    1984).

    3. Pham Mau Quan (Universite Paris XIII, ): 1) Infinitesimal Automorphisms

    and Characterizations of the Cotangent Bundles. 2) Stability of Periodic Orbits and

    Poincares Isometric Problem ( 1985).

    4. A. ASADA: Characteristic Classes in Non-commutative Geometry ( 1993).

    5. A. Asada: Non-commutative Version of Monodromy Theory ( 1994).

    6. M. Anastasiei (University Al I. Cuza , Iasi - ): Introduction to Lagrange

    Spaces ( 1995).

    7. K. Buchner (Technical University, Munchen - ): Differential Spaces: a Ge-

    neralization of Differential Manifolds ( 1996).

    8. W. Mozgawa (University Marie Curie, Lublin - ): Foliation theory and

    projective structures ( 1998).

    9. C.T.J. Dodson (University of Manchester, UK): Information geometric Riemannian

    neighbourhoods of randomness and independence ( 2005).

    2.3.

    , , :

    Colloquium on Differential Geometry, Janos Bolyai Mathematical Society, Budapest

    (3 7 1979). : Conjugate connections and differential

    equations.

    6

  • CSSR - GDR - Polish Conference on Differential Geometry and its Applications,

    Nove Mesto na Morave (8 12 1980). -

    : Linear connections on bundles over S1.

    7 , , (19 23

    1983). : On applications of related connections.

    3rd International Congress of Differential Geometry, (16

    1 1991). : Some applications of conjugate conne-

    ctions.

    1 , (27 28 1994).

    : .

    24th National Conference of Geometry and Topology, Timisoara (5 9 1994).

    : On a type of total differential equations in Frechet spaces (

    . ).

    2 , , (1 3 -

    1995). : .

    25th National Conference of Geometry and Topology, Univ. Al. I. Cusa, Iasi (18

    23 1995). : From principal connections to connections

    on principal sheaves.