Spatii riemann izometrice

CUPRINS
INTRODUCERE.................................................................
....................................3
CAPITOLUL                  I                   –                   VARIETĂŢI
DIFERENŢIABILE..........................................7
                            Varietaţi                        diferenţiabile.
Exemple....................................................................7
                                                                   Aplicaţii
diferenţiabile..............................................................
.....................13
                                                                     Vectori
tangenţi....................................................................
.........................15
              Diferenţiala          unei          aplicaţii          într-un
punct.......................................................19
                                                                     Vectori
cotangenţi..................................................................
.......................21
        Tensori   de   tip   (r,   s)   pe   o   varietate    diferenţiabilă
M......................................22
                                                                     Algebre
Lie.........................................................................
...........................24
                                                                       Forme
diferenţiale................................................................
.........................26
           Grupuri      de      transformări      cu      un       parametru
...................................................28
                                  Spaţii                             fibrate
vectoriale..................................................................
...............29
                      Conexiuni                  în                  fibrate
vectoriale..................................................................
....30
CAPITOLUL                   II                   –                    SPAŢII
RIEMANN...............................................................32
                               Definiţie.                           Exemple.
Proprietăţi.................................................................
....32
                    Tensorul               Riemann.               Definiţie.
Proprietăţi......................................................33
                    Tensorul                Ricci.                Definiţie.
Proprietăţi............................................................34
                                                                      Spaţii
Einstein....................................................................
...........................34
                 Spaţii            Riemann            de             curbură
constantă...........................................................35
                Tensorul            conform            de            curbură
Weyl...............................................................38
               Operatori          diferenţiali           pe           spaţii
Riemann......................................................42
CAPITOLUL            III            –             SPAŢII             RIEMANN
IZOMETRICE..................................47
            Spaţii        Riemann        izometrice        de        curbură
constantă.........................................47
                     Inversiuni                 între                 spaţii
Riemann.....................................................................
48
Aplicaţii...................................................................
......................................51
              Proprietăţi         spectrale         ale         varietăţilor
izometrice...........................................54
BIBLIOGRAFIE................................................................
...................................57