Geodesic
Invariants and flow geometry
Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 33-50 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow $ℱ_ξ$ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g,$ℱ_ξ$), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization of Killing-transversally symmetric spaces by using the curvature tensor of special flow model spaces. All these results extend the corresponding theory in Sasakian geometry to flow geometry.
DOI : 10.4064/cm-81-1-33-50
Keywords: flow model spaces, normal, contact and curvature homogeneous flows, invariants and characterizations of special Riemannian manifolds, flows generated by a unit Killing vector field

J. González-Dávila 1 ; L. Vanhecke 1

1 
@article{10_4064_cm_81_1_33_50,
     author = {J. Gonz\'alez-D\'avila and L. Vanhecke},
     title = {Invariants and flow geometry},
     journal = {Colloquium Mathematicum},
     pages = {33--50},
     year = {1999},
     volume = {81},
     number = {1},
     doi = {10.4064/cm-81-1-33-50},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-33-50/}
}
TY  - JOUR
AU  - J. González-Dávila
AU  - L. Vanhecke
TI  - Invariants and flow geometry
JO  - Colloquium Mathematicum
PY  - 1999
SP  - 33
EP  - 50
VL  - 81
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-33-50/
DO  - 10.4064/cm-81-1-33-50
LA  - en
ID  - 10_4064_cm_81_1_33_50
ER  - 
%0 Journal Article
%A J. González-Dávila
%A L. Vanhecke
%T Invariants and flow geometry
%J Colloquium Mathematicum
%D 1999
%P 33-50
%V 81
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-33-50/
%R 10.4064/cm-81-1-33-50
%G en
%F 10_4064_cm_81_1_33_50
J. González-Dávila; L. Vanhecke. Invariants and flow geometry. Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 33-50. doi: 10.4064/cm-81-1-33-50

Cité par Sources :