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## Colloquium Mathematicum

1996 | 71 | 2 | 253-262
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
253-262
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-09-26
Twórcy
autor
• Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Bibliografia
• [1] E. Boeckx, J. Gillard and L. Vanhecke, Semi-symmetric and semi-parallel geodesic spheres and tubes, Indian J. Pure Appl. Math., to appear.
• [2] B. Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Angew. Math. 325 (1981), 28-67.
• [3] M. Djorić and L. Vanhecke, Almost Hermitian geometry, geodesic spheres and symmetries, Math. J. Okayama Univ. 32 (1990), 187-206.
• [4] L. Gheysens and L. Vanhecke, Total scalar curvature of tubes about curves, Math. Nachr. 103 (1981), 177-197.
• [5] A. Gray, Tubes, Addison-Wesley, Reading, 1989.
• [6] A. Gray and L. Vanhecke, Riemannian geometry as determined by the volumes of small geodesic balls, Acta Math. 142 (1979), 157-198.
• [7] A. Gray and L. Vanhecke, The volumes of tubes about curves in a Riemannian manifold, Proc. London Math. Soc. 44 (1982), 215-243.
• [8] S. Tanno, Constancy of holomorphic sectional curvature in almost Hermitian manifolds, Kōdai Math. Sem. Rep. 25 (1973), 190-201.
• [9] L. Vanhecke, Geometry in normal and tubular neighborhoods, Rend. Sem. Fac. Sci. Univ. Cagliari, Supplemento al Vol. 58 (1988), 73-176.
• [10] L. Vanhecke and T. J. Willmore, Interaction of tubes and spheres, Math. Ann. 263 (1983), 31-42.
• [11] K. Yano and M. Kon, Structures on Manifolds, Ser. in Pure Math. 3, World Sci., Singapore, 1984.
Typ dokumentu
Bibliografia
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