Structure theorems on Riemannian spaces satisfying $R(X,\,Y)\cdot R=0$. I. The local version

[1] K. Abe, Relative curvatures and some applications to submanifolds in space forms, Thesis, Brown University, 1970.

[2] E. Cartan, Lecons sur la geometrie des espaces de Riemann, 2nd ed., Paris, 1946.

[3] R. Couty, Sur les transformations definis par le groupe de tolonomie infinitesimale, C. R. Acad. Sci. Paris 244 (1957) 553-555.

[4] R. Couty, Sur les transformations des varietes riemanniennes et kahleriennes, Ann. Inst. Fourier (Grenoble) 9 (1959) 147-248.

[5] D. Ferns, Totally geodesic foliations, Math. Ann. 188 (1970) 313-316.

[6] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.

[7] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 1, Wiley, New York, 1963.

[8] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. 2, Wiley, New York, 1969.

[9] P. I. Kovaljev, O ne katorih sojstah structuri, opredelaemoj tenzoram Rimana na prostranste affinnoj sajznocti, Ukrain. Geometr. Sb. 13 (1973) 95-100.

[10] P. I. Kovaljev, Ob adnom klasse rimanoih proctranstih, Tezisi Dokladov u Vseojuz. Konferencii po Sovremennim Problemam Geometrii, Samarkand, 1972, 95.

[11] P. I. Kovaljev, O ne katorih strukturi, opredelaemoj tenzoram Riamna na prostranste affinnoj sjaznosti (referat), Ukrain. Geometr. Sb. 13 (1973).

[12] N. H. Kuiper and S. S. Chern, Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space, Ann. of Math. 56 (1952) 422-430.

[13] A. Lichnerowicz, Courbure, nombres de Betti et espaces symmetriques, Proc. Internat. Congress Math. (Cambridge, 1950), Amer. Math. Soc, Vol. II, 1952, 216-223.

[14] M. Maltz, The nullity spaces of the curvature operator, Topologie et geometrie differentielle, Centre Nat. Recherche Sci., Paris, Vol. 8, 1966, 20.

[15] K. Nomizu, On hypersurfaces satisfying a certain condition on the curvature tensor, Tohoku Math. J. 20 (1968) 46-59.

[16] K. Sekigawa, On A-dimensional connected Einstein spaces satisfying the condition R(X, Y) R = 0, Sci, Rep. Niigata Univ. Ser. A, 7 (1969) 29-31.

[17] K. Sekigawa, On some 3-dimensional complete Riemannian manifolds satisfying R(X, Y) R = 0, Tohoku Math. J. 27 (1975) 561-568.

[18] J. Simons, On transitivity of holonomy systems, Ann. of Math. 76 (1962) 213-234.

[19] N. S. Sinjukov, O geodeziceskom otobrazenii rimanovih prostranstv, Trudy Vsesojuz. Mat. Sezda, 1956, 167-168.

[20] N. S. Sinjukov, Ob odnom klasse rimanovih prostranstv, Naucn. Ezegodnik OGI, Fiz.-Mat., F.-T. i In.-T. Fiziki, vip. 2, 1961, 122-126.

[21] N. S. Sinjukov, Poctu simmetriceskie romanovi proctranctva, Pervaja Vsesojuz. Geometr. Konferencia, Tezisi Dokladov, Kiev, 1962, 84.

[22] H. Takagi, An example of Riemann manifold satisfying R(X, Y) R = 0 but not VR --0, Tohoku Math. J. 24 (1972) 105-108.

[23] S. Tanno, A class of Riemannian manifolds satisfying R(X, Y) R = 0, Nagoya Math. J. 42 (1971) 67-77.

[24] S. Tanno, Hypersurfaces satisfying a certain condition on the Ricci tensor, Tohoku Math. J. 21 (1969) 297-303.

[25] S. Tanno, A theorem on totally geodesic foliations and its applications, Tensor 24 (1972) 116-122.