kemsuСибСкриптSibScript2949-21222949-2092Kemerovo State Universitykemsu-3953Research ArticleСтатьиСОЛИТОНЫ РИЧЧИ В КОНТАКТНЫХ МЕТРИЧЕСКИХ МНОГООБРАЗИЯХRICCI SOLITONS IN CONTACT METRIC MANIFOLDSТрипатхиМукут МаниTripathiMukut Manimmtripathi66@yahoo.comБенаресский индуистский университет, Варанаси, ИндияРоссияBanaras Hindu University, Varanasi, IndiaRussian Federation20112310201103-1181186Copyright © Трипатхи М.М., 20112011Трипатхи М.М.Tripathi M.M.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.sibscript.ru/jour/article/view/3953солитоны РиччиN (к)-контактные метрические многообразияK-контактные многообразиямногообразия СасакиRicci solitonN(k)-contact metric manifoldK-contact manifoldSasakian manifoldReferencesArnold, V. I. Contact geometry: the geometrical method of Gibb's thermodynamics/ V. I. Arnold // Proceedings of the Gibbs Symposium, Yale University, (May 15-17, 1989). American Mathematical Society. - 1990. - P. 163 - 179.Arnold, V. I. Contact geometry: the geometrical method of Gibb's thermodynamics/ V. I. Arnold // Proceedings of the Gibbs Symposium, Yale University, (May 15-17, 1989). American Mathematical Society. - 1990. - P. 163 - 179.Blair, D. E. Two remarks on contact metric structures / D. E. Blair // Tohoku Math. J. - 1977. - Vol. 29. - P. 319 - 324.Blair, D. E. Two remarks on contact metric structures / D. E. Blair // Tohoku Math. J. - 1977. - Vol. 29. - P. 319 - 324.Blair, D. E. Riemannian geometry ofcontact and symplectic manifolds / D. E. Blair. - Progress in Mathematics, 203. - Birkhauser Boston, Inc.: Boston, MA, 2002.Blair, D. E. Riemannian geometry ofcontact and symplectic manifolds / D. E. Blair. - Progress in Mathematics, 203. - Birkhauser Boston, Inc.: Boston, MA, 2002.Baikoussis, C. A decomposition of the curvature tensor of a contact manifold satisfying R(X,Y)£ = ^(Y)X - )Y) / C. Baikoussis, D. E. Blair and T. Koufogiorgos. - Mathematics Technical Report, University of Ioannina, Greece, 1992.Baikoussis, C. A decomposition of the curvature tensor of a contact manifold satisfying R(X,Y)£ = ^(Y)X - )Y) / C. Baikoussis, D. E. Blair and T. Koufogiorgos. - Mathematics Technical Report, University of Ioannina, Greece, 1992.Blair, D. E. Contact metric manifolds satisfying a nullity condition / D. E. Blair, T. Koufogiorgos and B. J. Papantoniou // Israel J. Math. - 1995. Vol. 91, no. 1-3. - P. 189 - 214.Blair, D. E. Contact metric manifolds satisfying a nullity condition / D. E. Blair, T. Koufogiorgos and B. J. Papantoniou // Israel J. Math. - 1995. Vol. 91, no. 1-3. - P. 189 - 214.Blair, D.E. On the concircular curvature tensor ofa contact metric manifold / D.E. Blair, J.-S. Kim and M.M. Tripathi // J. Korean Math. Soc. - 2005. - Vol. 42, no. 5. - P. 883 - 892.Blair, D.E. On the concircular curvature tensor ofa contact metric manifold / D.E. Blair, J.-S. Kim and M.M. Tripathi // J. Korean Math. Soc. - 2005. - Vol. 42, no. 5. - P. 883 - 892.Boeckx, E. A full classification of contact metric (к, j)-spaces/ E. Boeckx // Illinois J. Math. -2000. - Vol. 44, no. 1. - P. 212 - 219.Boeckx, E. A full classification of contact metric (к, j)-spaces/ E. Boeckx // Illinois J. Math. -2000. - Vol. 44, no. 1. - P. 212 - 219.Boyer, C. P. Einstein manifolds and contact geometry/ C. P. Boyer and K. Galicky // Proc. Amer. Math. Soc. - 2001. - Vol. 129. - P. 2419 - 2430.Boyer, C. P. Einstein manifolds and contact geometry/ C. P. Boyer and K. Galicky // Proc. Amer. Math. Soc. - 2001. - Vol. 129. - P. 2419 - 2430.Chave, T. Quasi-Einstein metrics and their renoirmalizability properties / T. Chave and G. Valent // Helv. Phys. Acta. - 1996. - Vol. 69. - P. 344 - 347.Chave, T. Quasi-Einstein metrics and their renoirmalizability properties / T. Chave and G. Valent // Helv. Phys. Acta. - 1996. - Vol. 69. - P. 344 - 347.Chave, T. On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties / T. Chave and G. Valent // Nuclear Phys. - 1996. - Vol. B 478. -Chave, T. On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties / T. Chave and G. Valent // Nuclear Phys. - 1996. - Vol. B 478. -P. 758 - 778.P. 758 - 778.Chern, S. S. Pseudo-groups continus infinis/ S. S. Chern // Colloques Internationaux du C. N. R. S., Strassbourg. - P. 119 - 136.Chern, S. S. Pseudo-groups continus infinis/ S. S. Chern // Colloques Internationaux du C. N. R. S., Strassbourg. - P. 119 - 136.Chow, B. The Ricci flow: An introduction/ B. Chow and D. Knoff. - Mathematical Surveys and Monographs 110, American Math. Soc., 2004.Chow, B. The Ricci flow: An introduction/ B. Chow and D. Knoff. - Mathematical Surveys and Monographs 110, American Math. Soc., 2004.Clifton, Y.H. The к-nullity space of curvature operator/ Y.H. Clifton and R. Maltz // Michigan Math. J. - 1970. - Vol. 17. - P. 85 - 89.Clifton, Y.H. The к-nullity space of curvature operator/ Y.H. Clifton and R. Maltz // Michigan Math. J. - 1970. - Vol. 17. - P. 85 - 89.Derdzinski, A. Compact Ricci solitons, Preprint.Derdzinski, A. Compact Ricci solitons, Preprint.Friedan, D. H. Nonlinear models in 2 + e dimensions / D. H. Friedan // Ann. Physics. - 1985. - Vol. 163. - P. 318 - 419.Friedan, D. H. Nonlinear models in 2 + e dimensions / D. H. Friedan // Ann. Physics. - 1985. - Vol. 163. - P. 318 - 419.Geiges, H. A briefhistory ofcontact geometry and topology/ H. Geiges // Expo. Math. - 2001. - Vol. 19, no. 1. -P. 25 - 53.Geiges, H. A briefhistory ofcontact geometry and topology/ H. Geiges // Expo. Math. - 2001. - Vol. 19, no. 1. -P. 25 - 53.Gray, J. W.Some global properties of contact structures / J. W. Gray // Ann. of Math. - 1959. - Vol. 69. - P. 421 - 450.Gray, J. W.Some global properties of contact structures / J. W. Gray // Ann. of Math. - 1959. - Vol. 69. - P. 421 - 450.Hamilton, R. S. The Ricci flow on surfaces/ R. S. Hamilton // Mathematics and general relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math. 71, American Math. Soc., 1988.Hamilton, R. S. The Ricci flow on surfaces/ R. S. Hamilton // Mathematics and general relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math. 71, American Math. Soc., 1988.Ivey, T. Ricci solitons on compact 3-manifolds/ T. Ivey // Differential Geom. Appl. -1993. - Vol. 3. - P. 301 - 307.Ivey, T. Ricci solitons on compact 3-manifolds/ T. Ivey // Differential Geom. Appl. -1993. - Vol. 3. - P. 301 - 307.Koufogiorgos, T. Contact metric manifolds/ T. Koufogiorgos // Ann. Global Anal. Geom. - 1993. - Vol. 11. - P. 25 - 34.Koufogiorgos, T. Contact metric manifolds/ T. Koufogiorgos // Ann. Global Anal. Geom. - 1993. - Vol. 11. - P. 25 - 34.MacLane, S. Geometrical mechanics II / S. MacLane. - Lecture notes, University of Chicago, 1968.MacLane, S. Geometrical mechanics II / S. MacLane. - Lecture notes, University of Chicago, 1968.Nazaikinskii, V. E. Contact geometry and linear differential equations / V. E. Nazaikinskii, V. E. Shatalov and B. Y. Sternin. - Walter de Gruyter, Berlin, 1992.Nazaikinskii, V. E. Contact geometry and linear differential equations / V. E. Nazaikinskii, V. E. Shatalov and B. Y. Sternin. - Walter de Gruyter, Berlin, 1992.Okumura, M. Some remarks on space with a certain contact structure / M. Okumura // Tohoku Math. J. - 1962. - Vol. 14. - P. 135 - 145.Okumura, M. Some remarks on space with a certain contact structure / M. Okumura // Tohoku Math. J. - 1962. - Vol. 14. - P. 135 - 145.Perelman, G. The entropy formula for the Ricci flow and its geometric applications/ G. Perelman. - Preprint, http://arXiv.org/abs/Math.DG/0211159.Perelman, G. The entropy formula for the Ricci flow and its geometric applications/ G. Perelman. - Preprint, http://arXiv.org/abs/Math.DG/0211159.Sasaki, S. On differentiable manifolds with certain structures which are closely related to almost contact structure. I / S. Sasaki // Tohoku Math. J. - 1960. - Vol. (2) 12. - P. 459 - 476.Sasaki, S. On differentiable manifolds with certain structures which are closely related to almost contact structure. I / S. Sasaki // Tohoku Math. J. - 1960. - Vol. (2) 12. - P. 459 - 476.Sasaki, S. On the differential geometry of tangent bundles of Riemannian manifolds II / S. Sasaki // Toohoku Math. J. - 1962. - Vol. (2) 14. - P. 146 - 155.Sasaki, S. On the differential geometry of tangent bundles of Riemannian manifolds II / S. Sasaki // Toohoku Math. J. - 1962. - Vol. (2) 14. - P. 146 - 155.Sasaki, S., Hatakeyama, Y. On differentiable manifolds with certain structures which are closely related to almost contact structure . II / S. Sasaki, Y. Hatakeyama // Toohoku Math. J. - 1961. - Vol. (2) 13. - P. 281 - 294.Sasaki, S., Hatakeyama, Y. On differentiable manifolds with certain structures which are closely related to almost contact structure . II / S. Sasaki, Y. Hatakeyama // Toohoku Math. J. - 1961. - Vol. (2) 13. - P. 281 - 294.Sharma, R. Certain results on K-contact and ( к, j) -contact manifolds/ R. Sharma //, J. Geom. -2008. - Vol. 89, no. 1 - 2. - P. 138 - 147.Sharma, R. Certain results on K-contact and ( к, j) -contact manifolds/ R. Sharma //, J. Geom. -2008. - Vol. 89, no. 1 - 2. - P. 138 - 147.Sharma, R. Sasakian 3-manifold as a Ricci Soliton represents the Heisenberg group / R. Sharma, A. Ghosh // International Journal of Geometric Methods in Modern Physics. - 2011. - Vol. 8, no. 1. - P. 149 - 154.Sharma, R. Sasakian 3-manifold as a Ricci Soliton represents the Heisenberg group / R. Sharma, A. Ghosh // International Journal of Geometric Methods in Modern Physics. - 2011. - Vol. 8, no. 1. - P. 149 - 154.Tanno, S. The topology of contact Riemannian manifolds / S. Tanno // Illinois J. Math. - 1968. - Vol. 12. - P. 700 - 717.Tanno, S. The topology of contact Riemannian manifolds / S. Tanno // Illinois J. Math. - 1968. - Vol. 12. - P. 700 - 717.Tanno, S. Some differential equations on Riemannian manifolds / S. Tanno // J. Math. Soc. Japan. - 1978. - Vol. 30. - P. 509 - 531.Tanno, S. Some differential equations on Riemannian manifolds / S. Tanno // J. Math. Soc. Japan. - 1978. - Vol. 30. - P. 509 - 531.Tanno, S. Ricci curvatures of contact Riemannian manifolds / S. Tanno // Toohoku Math. J. - 1988. - Vol. 40. - P. 441 - 448.Tanno, S. Ricci curvatures of contact Riemannian manifolds / S. Tanno // Toohoku Math. J. - 1988. - Vol. 40. - P. 441 - 448.Tashiro, Y. On contact structure of tangent sphere bundles / Y. Tashiro // Toohoku Math. J. -1969. - Vol. 21. - P. 117- 143.Tashiro, Y. On contact structure of tangent sphere bundles / Y. Tashiro // Toohoku Math. J. -1969. - Vol. 21. - P. 117- 143.Tripathi, M. M. and Kim, J.-S. On the concircular curvature tensor of a (K, J) -manifold/ M. M. Tripathi and J.-S. Kim // Balkan J. Geom. Appl. - 2004. - Vol. 9, no. 1. - P. 114 - 124.Tripathi, M. M. and Kim, J.-S. On the concircular curvature tensor of a (K, J) -manifold/ M. M. Tripathi and J.-S. Kim // Balkan J. Geom. Appl. - 2004. - Vol. 9, no. 1. - P. 114 - 124.
The authors declare that there are no conflicts of interest present.