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Year 2020, , 165 - 169, 15.10.2020
https://doi.org/10.36753/mathenot.683478

Abstract

References

  • Blair, D.E., Contact manifolds in Reimannian geometry, Lecture notes in Math. 509, Springer-Verlag., 1976.
  • Boyer, C.P., Galicki, K., Einstein manifold and contact geometry. Proc. Amer. Math. Soc., 129 (2001), 2419-2430.
  • Chrusciel, P. T., Reall, H. S., Tod, P., On non-existence of static vacuum black holes with degenerate components of the event horizon, Classical Quantum Gravity, 23 (2006), 549-554.
  • Deshmukh, S., Aloden, H., A note on Ricci soliton, Balkan J. of Geom. and Appl., 16 (2011), 48-55.
  • Deshmukh, S., Jacobi-type vector fields on Ricci solitons, Bull. Mathematique de la societe des sciences Mathematiques de Roumanie Nouvelle Series., 103 (2012), 41-50.
  • De, U.C. and Biswas, S., On K-contact eta-Einstein manifolds. Bull. Soc. Math., 16 (1990), 23-28.
  • De, U.C., De, A., On some curvature properties of K-contact manifolds. Extracta Math., 27 (2012), 125-134.
  • Guha, N. and De, U.C., On K-contact manifolds. Serdica-Bulgaricae Math. Publ., 19 (1993), 267-272.
  • Jezierski, J., On the existance of Kundts metrics and degenerate (or extremal) Killing horizones, , Classical Quantum Gravity, 26(2009), 035011, 11pp.
  • Jun, J. B., Kim, U. K., On 3-dimensional almost contact metric manifolds, Kyungpook Math. J., 34(1994), 293-301.
  • Koufogiorgos, T., Contact metric manifolds. Ann. Global Anal. Geom., 11 (1993), 25-34.
  • Mekki, M. E., Cherif, A. M., Generalised Ricci solitons on Sasakian manifolds, Kyungpook Math. J., 57 (2017)677-682.
  • Nurowski. P., Randall, M., Generalised Ricci solitons, J Geom. Anal., 26(2016), 1280-1345.
  • Prasad, R., Srivastava, V., On phi-symmetric K-contact manifolds. IJRRAS, 16 (2013), 104-110.
  • Sasaki, S., Lecture notes on almost contact manifolds, Part I. Tohoku Univ., $(1965)$.
  • Tarafdar, D. and De, U.C., On K-contact manifolds. Bull. Math. de la Soc. Sci. Math de Roumanie, 37 (1993), 207-215.
  • Yano, K. and Kon, M., Structures on manifolds. Vol 40, World Scientific Press, 1989.
  • Yildiz, A. and Ata, E., On a type of K-contact manifolds. Hacettepe J. Math. Stat., 41 (2012), 567-571.

Generalized Ricci Solitons on K-contact manifolds

Year 2020, , 165 - 169, 15.10.2020
https://doi.org/10.36753/mathenot.683478

Abstract

The object of the present paper is to study K-contact manifold admitting generalised Ricci solitons. We prove that a $K$-contact manifold of dimension $(2n+1)$ satisfying the generalised Ricci soliton equation is an Einstein one. Finally, we obtain several remarks.

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References

  • Blair, D.E., Contact manifolds in Reimannian geometry, Lecture notes in Math. 509, Springer-Verlag., 1976.
  • Boyer, C.P., Galicki, K., Einstein manifold and contact geometry. Proc. Amer. Math. Soc., 129 (2001), 2419-2430.
  • Chrusciel, P. T., Reall, H. S., Tod, P., On non-existence of static vacuum black holes with degenerate components of the event horizon, Classical Quantum Gravity, 23 (2006), 549-554.
  • Deshmukh, S., Aloden, H., A note on Ricci soliton, Balkan J. of Geom. and Appl., 16 (2011), 48-55.
  • Deshmukh, S., Jacobi-type vector fields on Ricci solitons, Bull. Mathematique de la societe des sciences Mathematiques de Roumanie Nouvelle Series., 103 (2012), 41-50.
  • De, U.C. and Biswas, S., On K-contact eta-Einstein manifolds. Bull. Soc. Math., 16 (1990), 23-28.
  • De, U.C., De, A., On some curvature properties of K-contact manifolds. Extracta Math., 27 (2012), 125-134.
  • Guha, N. and De, U.C., On K-contact manifolds. Serdica-Bulgaricae Math. Publ., 19 (1993), 267-272.
  • Jezierski, J., On the existance of Kundts metrics and degenerate (or extremal) Killing horizones, , Classical Quantum Gravity, 26(2009), 035011, 11pp.
  • Jun, J. B., Kim, U. K., On 3-dimensional almost contact metric manifolds, Kyungpook Math. J., 34(1994), 293-301.
  • Koufogiorgos, T., Contact metric manifolds. Ann. Global Anal. Geom., 11 (1993), 25-34.
  • Mekki, M. E., Cherif, A. M., Generalised Ricci solitons on Sasakian manifolds, Kyungpook Math. J., 57 (2017)677-682.
  • Nurowski. P., Randall, M., Generalised Ricci solitons, J Geom. Anal., 26(2016), 1280-1345.
  • Prasad, R., Srivastava, V., On phi-symmetric K-contact manifolds. IJRRAS, 16 (2013), 104-110.
  • Sasaki, S., Lecture notes on almost contact manifolds, Part I. Tohoku Univ., $(1965)$.
  • Tarafdar, D. and De, U.C., On K-contact manifolds. Bull. Math. de la Soc. Sci. Math de Roumanie, 37 (1993), 207-215.
  • Yano, K. and Kon, M., Structures on manifolds. Vol 40, World Scientific Press, 1989.
  • Yildiz, A. and Ata, E., On a type of K-contact manifolds. Hacettepe J. Math. Stat., 41 (2012), 567-571.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gopal Ghosh 0000-0001-6178-6340

U.c. De 0000-0002-8990-4609

Publication Date October 15, 2020
Submission Date February 2, 2020
Acceptance Date October 17, 2020
Published in Issue Year 2020

Cite

APA Ghosh, G., & De, U. (2020). Generalized Ricci Solitons on K-contact manifolds. Mathematical Sciences and Applications E-Notes, 8(2), 165-169. https://doi.org/10.36753/mathenot.683478
AMA Ghosh G, De U. Generalized Ricci Solitons on K-contact manifolds. Math. Sci. Appl. E-Notes. October 2020;8(2):165-169. doi:10.36753/mathenot.683478
Chicago Ghosh, Gopal, and U.c. De. “Generalized Ricci Solitons on K-Contact Manifolds”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 165-69. https://doi.org/10.36753/mathenot.683478.
EndNote Ghosh G, De U (October 1, 2020) Generalized Ricci Solitons on K-contact manifolds. Mathematical Sciences and Applications E-Notes 8 2 165–169.
IEEE G. Ghosh and U. De, “Generalized Ricci Solitons on K-contact manifolds”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 165–169, 2020, doi: 10.36753/mathenot.683478.
ISNAD Ghosh, Gopal - De, U.c. “Generalized Ricci Solitons on K-Contact Manifolds”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 165-169. https://doi.org/10.36753/mathenot.683478.
JAMA Ghosh G, De U. Generalized Ricci Solitons on K-contact manifolds. Math. Sci. Appl. E-Notes. 2020;8:165–169.
MLA Ghosh, Gopal and U.c. De. “Generalized Ricci Solitons on K-Contact Manifolds”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 165-9, doi:10.36753/mathenot.683478.
Vancouver Ghosh G, De U. Generalized Ricci Solitons on K-contact manifolds. Math. Sci. Appl. E-Notes. 2020;8(2):165-9.

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