A note on Kähler spacetime
DOI:
https://doi.org/10.5269/bspm.68796Resumen
In this paper we investigate the solitons on Kaehlerian spacetime manifolds admitting $m$-projective curvature and demonstrate the nature of solitons which depends on the relation between isotropic and anisotropic pressures, the cosmological constant, energy density, and gravitational constant.
Referencias
[1] Ahsan, Z, Siddiqui, S. A., Concircular curvature tensor and uid spacetime, Int. J. Theory Phys., v. 48, no. 11, 3202-3212,(2009).
[2] Barnes, A., Gen. Relat. Grav., no.4, 105-129, (1973).
[3] Blaga, A. M., On gradient η-Einstein solitons, Kragujevac J. Math., v. 42, no. 2, 229-237, (2018).
[4] Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., v. 61, no. 2, 205-212,(2009).
[5] Chaki, M. C., Roy, S., Spacetime with covariant constant energy momentum tensor, Int. J. Theory Phys., v. 35, 1027-1032, (1996).
[6] Chow, B., Lu, P., Ni, L., Hamiltons Ricci Flow, Graduate Studies in Mathematics ´ , American Mathematical Society, Providence, RI, USA, v. 77, no.2, (2006).
[7] Catino, G., Mazzieri, L., Gradient Einstein solitons, Nonlinear Anal., 132, pp. 66-94, (2016).
[8] Duggal, K. L., Curvature collineations and conservation laws of general relativity, in Presented at the Canadian Conference on General Relativity and Relativistic Astro-Physics, Halifax, 1985, Canada
[9] De, U. C, Mallick, S., Spcetime admitting m-projective curvature tensor e , Bulg. J. Phys, 39, pp. 331-338,(2012).
[10] De, U. C., Haseeb,A., On generalized Sasakian space form with m-projective curvature tensor e , Adv. Pure Appl. Math., 9 (1) (2018), 67-73.
[11] Duggal, K. L., Curvature inheritance symmetry in Riemannian spaces with applications to fluid spacetimes, Journal of Math. Phys., no. 33, v. 9, pp. 2989-2997,(1992).
[12] Ferus, D., Global Differential Geometry and Global Analysis, Springer-Verlag, New York, (1981).
[13] Hamilton, R. S., The Ricci ow on surfaces, Contemp. Math., v. 71, pp. 237-261, (1988).
[14] Kaigorodov, V. R., The curvature structure of spacetime, Prob. Geom, v. 14, 177-202, (1983).
[15] Kramer, D., Stephani, H., Herlt, E., MacCallum, M. H. A., Exact Solutions of Einstein’s Field Equations, Cambridge University Press, Cambridge, 1980.
[16] Katzin, H. G., Levine, J., Davis, W. R., Curvature collineations: A fundamental symmetry property of the spacetime of general relativity defined by the vanishing Lie derivative of the Riemannian curvature tensor, J. Math. Phys., v. 10, 617-629,(1969).
[17] Mallick ,S., Zhao, P., De, U. C., Spacetimes admitting quasi-conformal curvature tensor, Bull. Iranian Math. Soc, v. 42, no. 6, 1535-1546, (2016).
[18] Mallick, S., Suh, Y. J., De, U. C. A spacetime with pseudo-projective curvature tensor, J. Math. Phys., 57, 062501, (2016), doi: 10.1063/1.4952699.
[19] Mantica, C. A., De, U. C., Suh, Y. J., Molinari,L. G., Perfect fluid spacetimes with harmonic generalized curvature tensor, Osaka J. Math., 56, 173-182, (2019).
[20] Neill, B. O., Semi-Riemannian geometry with application to relativity, Pure and applied mathematics, Academic press,103, 1983, New York
[21] Narlikar, J. V., General Relativity and Gravitation, The Macmillan Company of India, 1978.
[22] Novello, M., Reboucas, M. J., The stability of a rotating universe, The Astrophysical Journal, 225, 719-724,(1978).
[23] Pokhariyal, G. P., Mishra, R. S., Curvature tensors and their relativistic significance, Yokohama Math. J., v. 19, no. 2, 97-103, (1971).
[24] Petrov, A. Z., Einstein spaces, Pergamon press, 1949, Oxford.
[25] Prakasha,D.,G., Amruthalakshmi, M. R., Mofarreh, F., Haseeb, A., Generalized Lorentzian Sasakian-space-forms with m-Projective curvature tensor e , Mathematics, 10(16) (2022), 12 pages
[26] Raychaudhary, A. K., Banerji, S., Banerjee, A., General relatively, Astrophysics and cosmology, Springer-Verlag, 1992.
[27] Srivastva, V., Pandey, N. P., On a perfect fluid Kaehler spacetime, Journal of Advances in Physics, v.3, no. 12, 4350-4355, (2016).
[28] Srivastava, S. K., General Ralativity and Cosmology, Prentice-Hall of India, Private Limited, New Delhi, 2008.
[29] Stephani, H., General Relativity: An Introduction to the theory of gravitational
field, Cambridge University Press, 1982, Cambridge
[30] Shaikh, A. A., Yoon, D. W., Hui, S. K., On quasi-Einstein spacetime, Tshukuba J. Maths, v. 33, 305-326,(2009).
[31] Yadav, S. K., Haseeb, A., Jamal, N., Almost pesudo symmetric Kahler manifolds admitting conformal Ricci-Yamabe metric, Int. J. Anal. Appl. 21:103 (2023).
[32] Yadav, S. K., Suthar, D. L., Kaehlerian Norden spacetime admitting conformal η-Ricci-Yamabe Metric, Int. J. of Geometric Methods in Modern Physics, https://doi.org/10.1142/S0219887824502347.
[33] Yadav, S. K., Chen, X., Z -tensor in mixed generalized quasi-Einstein GRW space-time, Sohag Journal of mathematics, v.11. no.1, 1-9, (2024).
[34] Yadav, S. K., Senway, S., Turki, N. B., Prasad, R., The Z -Tensor on Almost Co-Kahlerian Manifolds Admitting Riemann Soliton Structure, Advance in Mathematical Physics, Volume 2024, Article ID 7445240, 14 pages https://doi.org/10.1155/2024/7445240.
[35] Yadav, S. K., Suthar, D. L., Chaubey, S. K. , Almost conformal Ricci soliton on generalized Robertson walker-space time, Research in Mathematics vol.10, no.1, pp.1-10, (2023).
[36] Yadav, S. K., Ricci solitons on Para-Kaehler manifolds, Extracta Mathematikae, 34(2), 269-284, (2019).
[37] Zengin, F. O., m-projectively flat spacetime e , Math. Reports, 2, v.14, no. 64, 363-370, (2012).
[2] Barnes, A., Gen. Relat. Grav., no.4, 105-129, (1973).
[3] Blaga, A. M., On gradient η-Einstein solitons, Kragujevac J. Math., v. 42, no. 2, 229-237, (2018).
[4] Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., v. 61, no. 2, 205-212,(2009).
[5] Chaki, M. C., Roy, S., Spacetime with covariant constant energy momentum tensor, Int. J. Theory Phys., v. 35, 1027-1032, (1996).
[6] Chow, B., Lu, P., Ni, L., Hamiltons Ricci Flow, Graduate Studies in Mathematics ´ , American Mathematical Society, Providence, RI, USA, v. 77, no.2, (2006).
[7] Catino, G., Mazzieri, L., Gradient Einstein solitons, Nonlinear Anal., 132, pp. 66-94, (2016).
[8] Duggal, K. L., Curvature collineations and conservation laws of general relativity, in Presented at the Canadian Conference on General Relativity and Relativistic Astro-Physics, Halifax, 1985, Canada
[9] De, U. C, Mallick, S., Spcetime admitting m-projective curvature tensor e , Bulg. J. Phys, 39, pp. 331-338,(2012).
[10] De, U. C., Haseeb,A., On generalized Sasakian space form with m-projective curvature tensor e , Adv. Pure Appl. Math., 9 (1) (2018), 67-73.
[11] Duggal, K. L., Curvature inheritance symmetry in Riemannian spaces with applications to fluid spacetimes, Journal of Math. Phys., no. 33, v. 9, pp. 2989-2997,(1992).
[12] Ferus, D., Global Differential Geometry and Global Analysis, Springer-Verlag, New York, (1981).
[13] Hamilton, R. S., The Ricci ow on surfaces, Contemp. Math., v. 71, pp. 237-261, (1988).
[14] Kaigorodov, V. R., The curvature structure of spacetime, Prob. Geom, v. 14, 177-202, (1983).
[15] Kramer, D., Stephani, H., Herlt, E., MacCallum, M. H. A., Exact Solutions of Einstein’s Field Equations, Cambridge University Press, Cambridge, 1980.
[16] Katzin, H. G., Levine, J., Davis, W. R., Curvature collineations: A fundamental symmetry property of the spacetime of general relativity defined by the vanishing Lie derivative of the Riemannian curvature tensor, J. Math. Phys., v. 10, 617-629,(1969).
[17] Mallick ,S., Zhao, P., De, U. C., Spacetimes admitting quasi-conformal curvature tensor, Bull. Iranian Math. Soc, v. 42, no. 6, 1535-1546, (2016).
[18] Mallick, S., Suh, Y. J., De, U. C. A spacetime with pseudo-projective curvature tensor, J. Math. Phys., 57, 062501, (2016), doi: 10.1063/1.4952699.
[19] Mantica, C. A., De, U. C., Suh, Y. J., Molinari,L. G., Perfect fluid spacetimes with harmonic generalized curvature tensor, Osaka J. Math., 56, 173-182, (2019).
[20] Neill, B. O., Semi-Riemannian geometry with application to relativity, Pure and applied mathematics, Academic press,103, 1983, New York
[21] Narlikar, J. V., General Relativity and Gravitation, The Macmillan Company of India, 1978.
[22] Novello, M., Reboucas, M. J., The stability of a rotating universe, The Astrophysical Journal, 225, 719-724,(1978).
[23] Pokhariyal, G. P., Mishra, R. S., Curvature tensors and their relativistic significance, Yokohama Math. J., v. 19, no. 2, 97-103, (1971).
[24] Petrov, A. Z., Einstein spaces, Pergamon press, 1949, Oxford.
[25] Prakasha,D.,G., Amruthalakshmi, M. R., Mofarreh, F., Haseeb, A., Generalized Lorentzian Sasakian-space-forms with m-Projective curvature tensor e , Mathematics, 10(16) (2022), 12 pages
[26] Raychaudhary, A. K., Banerji, S., Banerjee, A., General relatively, Astrophysics and cosmology, Springer-Verlag, 1992.
[27] Srivastva, V., Pandey, N. P., On a perfect fluid Kaehler spacetime, Journal of Advances in Physics, v.3, no. 12, 4350-4355, (2016).
[28] Srivastava, S. K., General Ralativity and Cosmology, Prentice-Hall of India, Private Limited, New Delhi, 2008.
[29] Stephani, H., General Relativity: An Introduction to the theory of gravitational
field, Cambridge University Press, 1982, Cambridge
[30] Shaikh, A. A., Yoon, D. W., Hui, S. K., On quasi-Einstein spacetime, Tshukuba J. Maths, v. 33, 305-326,(2009).
[31] Yadav, S. K., Haseeb, A., Jamal, N., Almost pesudo symmetric Kahler manifolds admitting conformal Ricci-Yamabe metric, Int. J. Anal. Appl. 21:103 (2023).
[32] Yadav, S. K., Suthar, D. L., Kaehlerian Norden spacetime admitting conformal η-Ricci-Yamabe Metric, Int. J. of Geometric Methods in Modern Physics, https://doi.org/10.1142/S0219887824502347.
[33] Yadav, S. K., Chen, X., Z -tensor in mixed generalized quasi-Einstein GRW space-time, Sohag Journal of mathematics, v.11. no.1, 1-9, (2024).
[34] Yadav, S. K., Senway, S., Turki, N. B., Prasad, R., The Z -Tensor on Almost Co-Kahlerian Manifolds Admitting Riemann Soliton Structure, Advance in Mathematical Physics, Volume 2024, Article ID 7445240, 14 pages https://doi.org/10.1155/2024/7445240.
[35] Yadav, S. K., Suthar, D. L., Chaubey, S. K. , Almost conformal Ricci soliton on generalized Robertson walker-space time, Research in Mathematics vol.10, no.1, pp.1-10, (2023).
[36] Yadav, S. K., Ricci solitons on Para-Kaehler manifolds, Extracta Mathematikae, 34(2), 269-284, (2019).
[37] Zengin, F. O., m-projectively flat spacetime e , Math. Reports, 2, v.14, no. 64, 363-370, (2012).
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2025-09-22
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Cómo citar
Yadav, S. K. ., Suthar, D. L. ., & Srivastava, A. . (2025). A note on Kähler spacetime. Boletim Da Sociedade Paranaense De Matemática, 43, 1-14. https://doi.org/10.5269/bspm.68796
