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

Gillard, J.

Gillard, J.

Colloquium Mathematicae, Tome 70 (1996), p. 253-262 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that a connected complex space form ( $M^{n}$ ,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition ${\tilde{R}}_{X Y} \cdot \tilde{ϱ} = 0$ and by the semi-parallel condition ${\tilde{R}}_{X Y} \cdot σ = 0$ , 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 ${\tilde{R}}_{X Y}$ acts as a derivation.

Publié le : 1996-01-01

Zbl 0867.53054

EUDML-ID : urn:eudml:doc:210439

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     author = {Gillard, J.},
     title = {Characterizations of complex space forms by means of geodesic spheres and tubes},
     journal = {Colloquium Mathematicae},
     volume = {70},
     year = {1996},
     pages = {253-262},
     zbl = {0867.53054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv71i2p253bwm}
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Gillard, J. Characterizations of complex space forms by means of geodesic spheres and tubes. Colloquium Mathematicae, Tome 70 (1996) pp. 253-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv71i2p253bwm/

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