Geodesic
On the Sasaki metric of the normal bundle of a submanifold in a Riemannian space
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 157-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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On the normal bundle of a submanifold in a Riemannian space a natural Riemannian metric is introduced. The structure of surfaces with strongly parabolic normal bundle metric is determined. It is shown that the Sasaki metric of the normal bundle of vectors of fixed length of a two-dimensional Veronese surface has constant sectional curvature. Bibliography: 15 titles. 
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A. A. Borisenko; A. L. Yampol'skii. On the Sasaki metric of the normal bundle of a submanifold in a Riemannian space. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 157-175. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a10/

[1] Sasaki S., “On the differential geometry of tangent bundle of Riemannian manifold”, Tohoku Math. Journ., 10 (1958), 338–354 | DOI | MR | Zbl

[2] Chen B. G., Geometry of submanifolds, Dekker, M., 1973 | MR | Zbl

[3] Eizenkhart L., Rimanova geometriya, IL, M., 1948

[4] Reckziegel R., “On the eigenvalues of the shape operator of an isometric immersion into a space of constant curvature”, Math. Ann., 243 (1979), 71–82 | DOI | MR | Zbl

[5] Chern S., Kuiper K., “Some theorems of isometric imbeddings of compact Riemannian manifolds into Eucliadian spaces”, Ann. of Math., 53:3 (1952), 422–430 | DOI | MR

[6] Borisenko A. A., “O parabolicheskikh poverkhnostyakh v evklidovom prostranstve”, Ukr. geometr. sb., 25, Kharkov, 1982, 3–5 | MR | Zbl

[7] Kowalski O., “On the curvature of induced Riemannian metric on the tangent bundle of a Riemannian manifold”, Journ. reine angew. math., 250 (1971), 124–129 | MR | Zbl

[8] Borisenko A. A., Yampolskii A. L., “O stroenii kasatelnykh rassloenii mnogoobrazii s silno-parabolicheskoi metrikoi i silno-parabolicheskikh poverkhnostei”, Ukr. geometr. sb., 29, Kharkov, 1986, 12–32 | MR | Zbl

[9] Borisenko A. A., “O stroenii $l$-mernykh poverkhnostei s vyrozhdennoi vtoroi kvadratichnoi formoi v $n$-mernom evklidovom prostranstve”, Ukr. geometr. sb., 13, Kharkov, 1973, 18–27 | MR | Zbl

[10] Aminov Yu. A., “Kruchenie dvumernykh poverkhnostei v evklidovom prostranstve”, Ukr. geometr. sb., 17, Kharkov, 1975, 3–14 | Zbl

[11] Yampolskii A. L., “K geometrii sfericheskikh kasatelnykh rassloenii rimanovykh mnogoobrazii”, Ukr. geometr. sb., 24, Kharkov, 1981, 128–132

[12] Klingenberg W., Sasaki S., “Tangent sphere bundle of a 2-sphere”, Tohoku Math. Journ., 27 (1975), 45–57 | MR

[13] Yampolskii A. L., “Krivizna metriki Sasaki sfericheskikh kasatelnykh rassloenii”, Ukr. geometr. sb., 28, Kharkov, 1985, 132–145 | MR

[14] Blyashke V., Vvedenie v differentsialnuyu geometriyu, GITL, M., 1957

[15] Rozendorn E. R., “O polnykh poverkhnostyakh otritsatelnoi krivizny $k\leq1$ v evklidovykh prostranstvakh $E_3$, $E_4$”, Matem. sb., 58(100), 453–478 | MR | Zbl