Characterizations of complex space forms by means of geodesic spheres and tubes
Colloquium Mathematicum, Tome 71 (1996) no. 2, pp. 253-262
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that a connected complex space form ($M^n$,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition $\tilde{R}_{XY}·\tilde{ϱ}=0$ and by the semi-parallel condition $\tilde{R}_{XY}·σ=0$, considering special choices of tangent vectors $X,Y$ to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where $\tilde{R}$, $\tilde{ϱ}$ and $σ$ denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where $\tilde{R}_{XY}$ acts as a derivation.
@article{10_4064_cm_71_2_253_262,
author = {J. Gillard},
title = {Characterizations of complex space forms by means of geodesic spheres and tubes},
journal = {Colloquium Mathematicum},
pages = {253--262},
publisher = {mathdoc},
volume = {71},
number = {2},
year = {1996},
doi = {10.4064/cm-71-2-253-262},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-71-2-253-262/}
}
TY - JOUR AU - J. Gillard TI - Characterizations of complex space forms by means of geodesic spheres and tubes JO - Colloquium Mathematicum PY - 1996 SP - 253 EP - 262 VL - 71 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-71-2-253-262/ DO - 10.4064/cm-71-2-253-262 LA - en ID - 10_4064_cm_71_2_253_262 ER -
%0 Journal Article %A J. Gillard %T Characterizations of complex space forms by means of geodesic spheres and tubes %J Colloquium Mathematicum %D 1996 %P 253-262 %V 71 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm-71-2-253-262/ %R 10.4064/cm-71-2-253-262 %G en %F 10_4064_cm_71_2_253_262
J. Gillard. Characterizations of complex space forms by means of geodesic spheres and tubes. Colloquium Mathematicum, Tome 71 (1996) no. 2, pp. 253-262. doi: 10.4064/cm-71-2-253-262
Cité par Sources :