THE INVARIANTS OF GENERALIZED ????-TRANSFORMATIONS FOR ALMOST CONTACT METRIC STRUCTURES
https://doi.org/10.22405/2226-8383-2017-18-2-173-182
Abstract
In this paper we consider such generalizations of conformal transformations for contact metric manifolds as generalized conformal transformations, ????-transformations, generalized ????- transformations. Components of tensor fields for almost contact metric structure are given. These components are found in A-frame. Components for the tensor of affine deformation by Riemannian connection are calculated in this paper.We study six structure tensors of almost contact metric manifold.They are not invariant under generalized conformal transformations.We consider a particular case of the generalized conformal transformation, i.e. ????- transformation, third, fifth structure tensors are invariant under this transformation. Conditions of invariance for other structure tensors are received. The invariance of six structure tensors under generalized ????-transformations is studied. The second structure tensor is invariant under the generalized ????-transformation. Vanishing of third and fifth structure tensors is invariant under this transformation.We got the conditions of invariance under these transformations for first structured tensor under generalized ????-transformation.
About the Author
A. V. Nikiforova
Moscow Pedagogical State University
Russian Federation
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Geometry
Russian Federation
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Geometry
References
1. Smalley, L. L. 1986, "Brans-Dicke — type models with nonmetricity Phys. Rev. D., vol. 33, pp. 3590-3593.
2. Frolov, B. N. 2003, "Poincar´e-gauged calibration theory of gravitу MPGU, Moscow, 160 p.
3. Gambini, R. & Herrera, L. 1980, "Einstein Cartan theory in spin coefficient formalism J. Math. Phys., vol. 21, pp. 1449-1454.
4. Nich, H. T. 1982, "Spontaneously broken conformal gauge theory of gravitation Phys. Lett., vol. A88, pp. 388-390.
5. Obukhov, Ju. N. 1982, "Conformal invariance and space-time torsion Phys. Lett., vol. A90, pp. 13-16.
6. Gray, J. 1959, "Some global properties of contact structures Ann. Math., vol. 69, no.2, pp. 412- 450.
7. Chinea, D. & Marrero J. C. 1992, "Conformal changes of almost contact metric structures Riv. Mat. Univ. Parma., vol. 1, pp. 19-31.
8. Olszak, Z. 1989, "Locally conformal almost cosymplectic manifolds Colloq. Math., vol. 57, no. 1, pp. 73-87.
9. Kirichenko, V. F. & Levkovec, V. А. 2006, "On geometry of L-manifolds Mathematical Notes, vol. 79, no. 6, pp. 854-869.
10. Kirichenko, V. F. & Baklashova, N. S. 2007, "The geometry of contact Lee forms and a contact analog of Ikuta’s theorem Mathematical Notes, vol. 82, no. 3, pp. 347–360.
11. Kirichenko, V. F. & Dondukova, N. N. 2006, "Contactly geodesic transformations of almostcontact metric structures Mathematical Notes, vol. 80, no. 2, pp. 209–219.
12. Rodina, E. V. 1997, "Linear extensions of almost contact metric manifolds Diss. . . . kand. fis.- mat. nauk., MPGU, Moscow,98 p.
13. Ignatochkina, L. A. 2011, "Generalization for transformations of ???? 1 -bundle which induced by conformal transformations of their base Sb. Math., vol. 202, no. 5, pp. 665–682.
14. Kirichenko, V. F. 2013, "Differential geometric structure on manifolds:, 2, Pechatny Dom, Odessa, 458 p.
15. Kirichenko, V. F. & Uskorev, I. V. 2008, "Invariants of conformal transformations of almost contact metric structures Mathematical Notes, vol. 84, no. 6, pp. 783–794.
Review
For citations:
Nikiforova A.V. THE INVARIANTS OF GENERALIZED ????-TRANSFORMATIONS FOR ALMOST CONTACT METRIC STRUCTURES. Chebyshevskii Sbornik. 2017;18(2):173-182. (In Russ.) https://doi.org/10.22405/2226-8383-2017-18-2-173-182
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