# Characterizations of complex space forms by means of geodesic spheres and tubes

Colloquium Mathematicae (1996)

- Volume: 71, Issue: 2, page 253-262
- ISSN: 0010-1354

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topGillard, J.. "Characterizations of complex space forms by means of geodesic spheres and tubes." Colloquium Mathematicae 71.2 (1996): 253-262. <http://eudml.org/doc/210439>.

@article{Gillard1996,

abstract = {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.},

author = {Gillard, J.},

journal = {Colloquium Mathematicae},

keywords = {complex space forms; geodesic spheres; tubular hypersurfaces about geodesics},

language = {eng},

number = {2},

pages = {253-262},

title = {Characterizations of complex space forms by means of geodesic spheres and tubes},

url = {http://eudml.org/doc/210439},

volume = {71},

year = {1996},

}

TY - JOUR

AU - Gillard, J.

TI - Characterizations of complex space forms by means of geodesic spheres and tubes

JO - Colloquium Mathematicae

PY - 1996

VL - 71

IS - 2

SP - 253

EP - 262

AB - 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.

LA - eng

KW - complex space forms; geodesic spheres; tubular hypersurfaces about geodesics

UR - http://eudml.org/doc/210439

ER -

## References

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