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Almost Hermitian manifolds satisfying some curvature conditions. (English) Zbl 0423.53030


MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C30 Differential geometry of homogeneous manifolds
53C35 Differential geometry of symmetric spaces
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[1] W. AMBROSE AND I. M. SINGER, On homogeneous Riemanman manifolds, Duke Math. J., 25 (1958), 647-670. · Zbl 0134.17802
[2] J. E. D’ATRI AND H. K. NICKERSON, Geodesic symmetries in spaces with special curvature tensors, J. Diff. Geom., 9 (1970), 251-262. · Zbl 0285.53019
[3] S. FUJIMURA, A remark on Lichnerowicz’s theorem for locally symmetric Riemannian manifolds, Memoirs of the Research Institute of Science and Engineering, Ritsumeikan Univ., 27 (1974), 1-3.
[4] T. FUKAMI AND S. ISHIHARA, Almost Hermitian structure on SG, Thoku Math. J., 7 (1955), 151-156. · Zbl 0068.36001
[5] A. GRAY, Riemannian manifolds with geodesic symmetries of order 3, J. Diff. Geom., 7 (1972), 343-369. · Zbl 0275.53026
[6] A. GRAY, Kahler submanifolds of homogeneous almost Hermitian manifolds, Thoku Math. J., 21 (1969), 190-194. · Zbl 0194.22803
[7] S. KOBAYASHI, Transformation groups in Differential Geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1972. · Zbl 0246.53031
[8] S. KOBAYASHI AND K. NOMIZU, Foundations of Differential Geometry, I, II, Interscience Publishers, New York, 1963, 1969. · Zbl 0119.37502
[9] M. MATSUMOTO, On 6-dimensional almost Tachibana spaces, Tensor N. S., 23 (1972), 250-252. · Zbl 0236.53048
[10] K. NOMIZU AND K. YANO, Some results to the equivalent problem in Riemannian geometry, Proc. United States-Japan Sem. in Kyoto, Japan, 1965, 95-100. · Zbl 0151.28203
[11] Y. OGAWA, A condition for a compact Kaehlerian space to be locally symmetric, · Zbl 0364.53026
[12] S. SAWAKI AND K. SEKIGAWA, Almost Hermitian manifolds with constant holomorphic sectional curvature, J. Diff. Geom., 9 (1974), 123-143. · Zbl 0277.53036
[13] K. SEKIGAWA, Some hypersurfaces satisfying R(X, Y)R =0, Tensor N. S., 25 (1972), 133-136. · Zbl 0258.53043
[14] K. SEKIGAWA, On some 3-dimensional complete Riemannian manifolds satisfying R{X, Y).R=0, Thoku Math. J., 27 (1975), 561-568.} · Zbl 0321.53040
[15] K. SEKIGAWA, On some 4-dimensional Riemannian manifolds satisfying R{X, Y) R =0, Hokkaido Math, J., 2 (1977), 216-229.} · Zbl 0387.53013
[16] K. SEKIGAWA, Notes on homogeneous almost Hermitian manifolds, to appear in Hokkaido Math. J. . · Zbl 0388.53014
[17] K. SEKIGAWA AND H. TAKAGI, On conformally flat spaces satisfying a certain condition on the Ricci tensor, Thoku Math. J., 23 (1971), 1-11. · Zbl 0218.53056
[18] I. M. SINGER, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math., 13 (1960), 685-697. · Zbl 0171.42503
[19] H. TAKAGI, An example of Riemannian manifolds satisfying R(X, Y) R =0, but not F#=0, Thoku Math. J., 24 (1972), 105-108. · Zbl 0237.53041
[20] K. TAKAMATSU, Some properties of 6-dimensional i-spaces, Kdai Math. Sem. Rep., 23 (1971), 215-232. · Zbl 0222.53036
[21] F. TRICERRI AND L. VANHECKE, Flat almost Hermitian manifolds which are not Kahler manifolds, Tensor N. S., 31 (1977), 249-254. · Zbl 0375.53037
[22] E. TSUKADA, Transitive actions of compact connected Lie groups on symmetric spaces, Sci. Rep. Niigata Univ., 15 (1978), 1-19. · Zbl 0374.57010
[23] WATANABE AND K. TAKAMATSU, On a if-space of constant holomorphic sectional curvature, Kdai Math. Sem. Rep., 25 (1973), 297-306. · Zbl 0276.53029
[24] J. WOLF AND A. GRAY, Homogeneous spaces defined by Lie group automorphisms, I, II, J. Diff. Geom., 2 (1968), 77-114, 115-159. · Zbl 0169.24103
[25] S. YAMAGUCHI, G. CHOMAN AND M. MATSUMOTO, On a special almost Tachibana space, Tensor, N. S., 24 (1972), 351-354. · Zbl 0249.53038
[26] K. YANO, Differential geometry on complex and almost complex spaces, Pergamon Press, 1965. · Zbl 0127.12405
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