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Keywords:
generalized Riemannian space; infinitesimal bending; infinitesimal deformation; subspace
generalized Riemannian space; infinitesimal bending; infinitesimal deformation; subspace
Summary:
In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-sym\-metry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).
References:
[1] Efimov N. V.: Kachestvennye voprosy teorii deformacii poverhnostei. UMN 3.2 (1948), 47–158.
[2] Eisenhart L. P.: Generalized Riemann spaces. Proc. Nat. Acad. Sci. USA 37 (1951), 311–315. MR 0043530
[3] Kon-Fossen S. E.: Nekotorye voprosy differ. geometrii v celom. : Fizmatgiz, Moskva. 1959.
[4] Hineva S. T.: On infinitesimal deformations of submanifolds of a Riemannian manifold. Differ. Geom., Banach center publications 12, PWN, Warshaw, 1984, 75–81. MR 0961074 | Zbl 0556.53035
[5] Ivanova-Karatopraklieva I., Sabitov I. Kh.: Surface deformation. J. Math. Sci., New York, 70, 2 (1994), 1685–1716.
[6] Ivanova-Karatopraklieva I., Sabitov I. Kh.: Bending of surfaces II. J. Math. Sci., New York, 74, 3 (1995), 997–1043. MR 1330961 | Zbl 0861.53002
[7] Lizunova L. Yu.: O beskonechno malyh izgibaniyah giperpoverhnostei v rimanovom prostranstve. Izvestiya VUZ, Matematika 94, 3 (1970), 36–42. MR 0276901
[8] Markov P. E.: Beskonechno malye izgibanya nekotoryh mnogomernyh poverhnostei. Matemat. zametki T. 27, 3 (1980), 469–479. MR 0570757
[9] Mikeš J.: Holomorphically projective mappings and their generalizations. J. Math. Sci., New York, 89, 3 (1998), 1334–1353. MR 1619720 | Zbl 0983.53013
[10] Mikeš J., Laitochová J., Pokorná O.: On some relations between curvature and metric tensors in Riemannian spaces. Suppl. ai Rediconti del Circolo Mathematico di Palermo 2, 63 (2000), 173–176. Zbl 0978.53030
[11] Minčić S. M.: Ricci type identities in a subspace of a space of non-symmetric affine connexion. Publ. Inst. Math., NS, t.18(32) (1975), 137–148. MR 0383272
[12] Minčić S. M.: Novye tozhdestva tipa Ricci v podprostranstve prostranstva nesimmetrichnoi affinoi svyaznosty. Izvestiya VUZ, Matematika 203, 4 (1979), 17–27.
[13] Minčić S. M.: Derivational formulas of a subspace of a generalized Riemannian space. Publ. Inst. Math., NS, t.34(48) (1983), 125–135. MR 0770025
[14] Minčić S. M.: Integrability conditions of derivational formulas of a subspace of generalized Riemannian space. Publ. Inst. Math., NS, t.31(45) (1980), 141–157.
[15] Minčić S. M., Velimirović L. S.: O podprostranstvah obob. rimanova prostranstva. Siberian Mathematical Journal, Dep. v VINITI No.3472-V 98 (1998).
[16] Minčić S. M., Velimirović L. S.: Riemannian Subspaces of Generalized Riemannian Spaces. Universitatea Din Bacau Studii Si Cercetari Stiintifice, Seria: Matematica, 9 (1999), 111–128. MR 1848987 | Zbl 1056.53500
[17] Minčić S. M., Velimirović L. S., Stanković M. S.: Infinitesimal Deformations of a Non-Symmetric Affine Connection Space. Filomat (2001), 175–182.
[18] Velimirović L. S., Minčić S. M., Stanković M. S.: Infinitesimal deformations and Lie Derivative of a Non-symmetric Affine Connection Space. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42 (2003), 111–121. MR 2056026 | Zbl 1061.53010
[19] Mishra R. S.: Subspaces of generalized Riemannian space. Bull. Acad. Roy. Belgique, Cl. sci., (1954), 1058–1071. MR 0067551
[20] Prvanovich M.: Équations de Gauss d’un sous-espace plongé dans l’espace Riemannien généralisé. Bull. Acad. Roy. Belgique, Cl. sci., (1955), 615–621.
[21] Velimirović L. S., Minčić S. M.: On infinitesimal bendings of subspaces of generalized Riemannian spaces. Tensor (2004), 212–224.
[22] Yano K.: Sur la theorie des deformations infinitesimales. Journal of Fac. of Sci. Univ. of Tokyo 6 (1949), 1–75. MR 0035084 | Zbl 0040.37803
[23] Yano K.: Infinitesimal variations of submanifolds. Kodai Math. J., 1 (1978), 30–44. MR 0487913 | Zbl 0411.53037
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