Geodesic
Warped products, cones over Einstein spaces, and classification of Ric-semiparallel submanifolds of a~certain class
Izvestiya. Mathematics , Tome 67 (2003) no. 5, pp. 955-973.

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We consider warped products of Riemannian manifolds and some special cases. We give a classification for a class of normally flat Ric-semiparallel submanifolds in Euclidean spaces. 
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V. A. Mirzoyan. Warped products, cones over Einstein spaces, and classification of Ric-semiparallel submanifolds of a~certain class. Izvestiya. Mathematics , Tome 67 (2003) no. 5, pp. 955-973. http://geodesic.mathdoc.fr/item/IM2_2003_67_5_a4/

[1] Szabo Z. I., “Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$. I: The local version”, J. Diff. Geom., 17:4 (1982), 531–582 | MR | Zbl

[2] Szabo Z. I., “Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$. II: Global version”, Geom. Dedicata, 19 (1985), 65–108 | DOI | MR | Zbl

[3] Lumiste Yu. G., “Polusimmetricheskie podmnogoobraziya”, Itogi nauki i tekhn. Problemy geometrii, 23, VINITI, M., 1991, 3–28 | MR

[4] Mirzoyan V. A., “$\operatorname{Ric}$-polusimmetricheskie podmnogoobraziya”, Itogi nauki i tekhn. Problemy geometrii, 23, VINITI, M., 1991, 29–66 | MR

[5] Boeckx E., Kowalski O., Vanhecke L., Riemannian manifolds of conullity two, World Scientific, Singapore, 1996 | MR | Zbl

[6] Nomizu K., “On hypersurfaces satisfying a certain condition on the curvature tensor”, Tôhoku Math. J., 20:1 (1968), 46–59 | DOI | MR | Zbl

[7] Takagi H., “An example of Riemannian manifolds satisfying $R(X,Y)\cdot R=0$ but not $\nabla R=0$”, Tôhoku Math. J., 24:1 (1972), 105–108 | DOI | MR | Zbl

[8] Mirzoyan V. A., “Strukturnye teoremy dlya rimanovykh $\operatorname{Ric}$-polusimmetricheskikh prostranstv”, Izv. vuzov. Matematika, 1992, no. 6, 80–89 | MR | Zbl

[9] Mirzoyan V. A., “Obobscheniya teoremy Yu. Lumiste o poluparallelnykh podmnogoobraziyakh”, Izv. NAN Armenii. Matematika, 33:1 (1998), 53–64 | MR | Zbl

[10] Mirzoyan V. A., “Podmnogoobraziya s parallelnymi i poluparallelnymi strukturami”, Izv. NAN Armenii. Matematika, 34:5 (1999), 63–66 | MR | Zbl

[11] Mirzoyan V. A., “Klassifikatsiya $\operatorname{Ric}$-poluparallelnykh giperpoverkhnostei v evklidovykh prostranstvakh”, Matem. sb., 191:9 (2000), 65–80 | MR | Zbl

[12] Petrov A. Z., Prostranstva Einshteina, Fizmatgiz, M., 1961 | MR | Zbl

[13] Besse A., Mnogoobraziya Einshteina, 1, 2, Mir, M., 1990 | MR

[14] Chern S. S., Kuiper N., “Some theorems on the isometric imbedding of compact Riemannian manifolds in Euclidean space”, Ann. Math., 56:3 (1952), 422–430 | DOI | MR

[15] Shirokov P. A., Izbrannye raboty po geometrii, Izd-vo KGU, Kazan, 1996

[16] Kruchkovich G. I., “Ob odnom klasse rimanovykh prostranstv”, Tr. seminara po vekt. i tenz. analizu, 11, Izd-vo MGU, M., 1961, 103–128

[17] Bushop R., O'Neill B., “Manifolds of negative curvature”, Trans. Amer. Math. Soc., 145 (1969), 1–49 | DOI | MR

[18] Sekigawa K., “On the Riemannian manifolds of the form $B\times _fF$”, Kodai Math. Sem. Rep., 26 (1975), 343–347 | DOI | MR | Zbl

[19] Dillen F., Nölker S., “Semi-parallelity, multirotation surfaces and the helix property”, J. Rein. Angew. Math., 435 (1993), 33–63 | MR | Zbl

[20] Nölker S., “Izometric immersions of warped products”, Diff. Geom. Appl., 6 (1996), 1–30 | DOI | MR | Zbl

[21] Mirzoyan V. A., “Konusy nad einshteinovymi prostranstvami”, Izv. NAN Armenii, 33:5 (1998), 46–54 | MR | Zbl

[22] Rashevskii P. K., Rimanova geometriya i tenzornyi analiz, Nauka, M., 1964 | MR

[23] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya. Metody i prilozheniya, Nauka, M., 1986 | MR

[24] Postnikov M. M., Lektsii po geometrii. Semestr V. Rimanova geometriya, Faktorial, M., 1998

[25] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. II, Nauka, M., 1981

[26] Chen B.-Y., Geometry of submanifolds, Marcel Dekker, N. Y., 1973 | MR | Zbl

[27] Moor J. D., “Isometric immersions of Riemannian products”, J. Diff. Geom., 5 (1971), 159–168 | MR | Zbl

[28] Lumiste Yu. G., “Neprivodimye normalno ploskie polusimmetricheskie podmnogoobraziya, I”, Izv. vuzov. Matematika, 1990, no. 8, 45–53 | MR | Zbl

[29] Lumiste Yu. G., “Neprivodimye normalno ploskie polusimmetricheskie podmnogoobraziya, II”, Izv. vuzov. Matematika, 1990, no. 9, 31–40 | MR | Zbl