Previous |  Up |  Next


semi-symmetric spaces; Killing and Codazzi Ricci tensor; locally symmetric spaces; spaces with volume-preserving geodesic symmetries; C-spaces; Osserman spaces
One proves that semi-symmetric spaces with a Codazzi or Killing Ricci tensor are locally symmetric. Some applications of this result are given.
[BPV] Berndt, J., Prüfer, F., Vanhecke, L.: Symmetric-like Riemannian manifolds and geodesic symmetries. preprint. MR 1331561
[BV] Berndt, J., Vanhecke, L.: Two natural generalizations of locally symmetric spaces. Diff. Geom. Appl. 2 (1992), 57-80. MR 1244456
[B] Besse, A. L.: Einstein manifolds. Ergeb. Math. Grenzgeb. 3. Folge 10, Springer-Verlag, Berlin, Heidelberg, New York, 1987. MR 0867684 | Zbl 1147.53001
[Bo] Boeckx, E.: Asymptotically foliated semi-symmetric spaces. in preparation. Zbl 0846.53031
[BKV] Boeckx, E., Kowalski, O., Vanhecke, L.: Non-homogeneous relatives of symmetric spaces. Diff. Geom. Appl. (to appear).
[Ca] Cartan, E.: Leçons sur la géométrie des espaces de Riemann. 2nd edition, Paris, 1946. MR 0020842 | Zbl 0060.38101
[Ch] Cho, J. T.: Natural generalizations of locally symmetric spaces. Indian J. Pure Appl. Math. (to appear). MR 1218533 | Zbl 0772.53029
[D’AN] D’Atri, J. E., Nickerson, H. K.: Divergence-preserving geodesic symmetries. J. Diff. Geom. 3 (1969), 467-476. MR 0262969
[GSV] Gilkey, P., Swann, A., Vanhecke, L.: Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator. preprint. MR 1348819
[G] Gray, A.: Einstein-like manifolds which are not Einstein. Geom. Dedicata 7 (1978), 259-280. MR 0505561 | Zbl 0378.53018
[KN] Kobayashi, S., Nomizu, K.: Foundations of differential geometry I, II. Interscience Publishers, New York, 1963, 1969. MR 0152974
[K1] Kowalski, O.: Spaces with volume-preserving geodesic symmetries and related classes of Riemannian manifolds. Rend. Sem. Mat. Univ. Politec. Torino, Fascicolo Speciale Settembre (1983), 131–158. MR 0829002
[K2] Kowalski, O.: An explicit classification of 3-dimensional Riemannian spaces satisfying $\scriptstyle R(X,Y)\cdot R=0$. preprint. MR 1408298
[O] R. Osserman: Curvature in the eighties. Amer. Math. Monthly 97 (1990), 731-756. MR 1072814 | Zbl 0722.53001
[S] Sinjukov, N. S.: Geodesic maps on Riemannian spaces. (Russian), Publishing House “Nauka" Moscow, 1979. MR 0552022
[Sz1] Szabó, Z. I.: Structure theorems on Riemannian manifolds satisfying $\scriptstyle R(X,Y)\cdot R=0$, I,Local version. J. Diff. Geom. 17 (1982), 531-582. MR 0683165
[Sz2] Szabó, Z. I.: Structure theorems on Riemannian manifolds satisfying $\scriptstyle R(X,Y)\cdot R=0$, II, Global versions. Geom. Dedicata 19 (1985), 65-108. MR 0797152
[V1] Vanhecke, L.: Some solved and unsolved problems about harmonic and commutative spaces. Bull. Soc. Math. Belg., Sér. B 34 (1982), 1-24. MR 0683378 | Zbl 0518.53042
[V2] Vanhecke, L.: Geometry in normal and tubular neighborhoods. Lecture Notes, Proc. Workshop on Differential Geometry and Topology, Cala Gonone (Sardinia), Rend. Sem. Fac. Sci. Univ. Cagliari, Supplemento al Vol. 58 (1988), 73-176. MR 1122858
Partner of
EuDML logo