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Year 2020, Volume: 49 Issue: 6, 2007 - 2016, 08.12.2020
https://doi.org/10.15672/hujms.551596

Abstract

References

  • [1] V. Berestovskii and Y. Nikonorov, Killing vector fields of constant length on Riemannian manifolds, Siberian Math. J. 49 (3), 395–407, 2008.
  • [2] A.L. Besse, Einstein Manifolds, Springer Verlag, 1987.
  • [3] D.E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer Verlag, 1976.
  • [4] C. Boyer and K. Galicki, Einstein manifolds and contact geometry, Proc. Amer. Math. Soc. 129 (8), 2419–2430, 2001.
  • [5] B. Chow, P. Lu and L. Ni, Hamilton’s Ricci Flow, Graduate studies in Mathematics, 77, AMS Scientific Press, 2010.
  • [6] S. Deshmukh, Real hypersurfaces of a complex space form, Proc. Math. Sci. 121 (2), 171–179, 2011.
  • [7] S. Deshmukh, Jacobi-type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math. Roumanie 55 (103), No. 1, 41–50, 2012.
  • [8] A. Hurtado, Stability numbers in K-contact manifolds, Diff. Geom. Appl. 26 (3), 227–242, 2008.
  • [9] C.J.G. Manchado and J.D. Perez, On the structure vector field of a real hypersurface in complex two-plane Grassmannians, Cent. Eur. J. Math. 10 (2), 451–455, 2012.
  • [10] A. Mastromartino and Y. Villarroel, The annihilator of a K-contact manifold, Math. Rep. (Bucur.) 6 (56), 431–443, 2004.
  • [11] B.C Montano, A.D. Nikola, J.C. Marrero, and I. Yudin, Examples of compact K-contact manifolds with no Sasakian metric, Int. J. Geom. Methods Mod. Phys. 11 (9), 1460023, 10 pp., 2014.
  • [12] M. Okumura, Certain almost contact hypersurfaces in Kaehler manifolds of constant holomorphic sectional curvature, Tohoku Math. J. (2), 16, 270–284, 1964.
  • [13] Z. Olszak, On contact metric manifolds, Tohoku Math. J. (2), 31, 247–253, 1979.
  • [14] D. Perrone, Contact metric manifolds whose characteristic vector field is harmonic vector field, Differential Geom. Appl. 20, 367–378, 2004.
  • [15] T. Yamazaki, On a surgery of K-contact manifolds, Kodai Math. J. 24 (2), 214–225, 2001.
  • [16] T. Yamazaki, A construction of K-contact manifolds by a fiber join, Tohoku Math. J. (2), 51 (4), 433–446, 1999.
  • [17] A. Yildiz and E. Ata, On a type of K-contact manifolds, Hacet. J. Math. Stat. 41 (4), 567–571, 2012.

A note on contact metric manifolds

Year 2020, Volume: 49 Issue: 6, 2007 - 2016, 08.12.2020
https://doi.org/10.15672/hujms.551596

Abstract

In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.

References

  • [1] V. Berestovskii and Y. Nikonorov, Killing vector fields of constant length on Riemannian manifolds, Siberian Math. J. 49 (3), 395–407, 2008.
  • [2] A.L. Besse, Einstein Manifolds, Springer Verlag, 1987.
  • [3] D.E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer Verlag, 1976.
  • [4] C. Boyer and K. Galicki, Einstein manifolds and contact geometry, Proc. Amer. Math. Soc. 129 (8), 2419–2430, 2001.
  • [5] B. Chow, P. Lu and L. Ni, Hamilton’s Ricci Flow, Graduate studies in Mathematics, 77, AMS Scientific Press, 2010.
  • [6] S. Deshmukh, Real hypersurfaces of a complex space form, Proc. Math. Sci. 121 (2), 171–179, 2011.
  • [7] S. Deshmukh, Jacobi-type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math. Roumanie 55 (103), No. 1, 41–50, 2012.
  • [8] A. Hurtado, Stability numbers in K-contact manifolds, Diff. Geom. Appl. 26 (3), 227–242, 2008.
  • [9] C.J.G. Manchado and J.D. Perez, On the structure vector field of a real hypersurface in complex two-plane Grassmannians, Cent. Eur. J. Math. 10 (2), 451–455, 2012.
  • [10] A. Mastromartino and Y. Villarroel, The annihilator of a K-contact manifold, Math. Rep. (Bucur.) 6 (56), 431–443, 2004.
  • [11] B.C Montano, A.D. Nikola, J.C. Marrero, and I. Yudin, Examples of compact K-contact manifolds with no Sasakian metric, Int. J. Geom. Methods Mod. Phys. 11 (9), 1460023, 10 pp., 2014.
  • [12] M. Okumura, Certain almost contact hypersurfaces in Kaehler manifolds of constant holomorphic sectional curvature, Tohoku Math. J. (2), 16, 270–284, 1964.
  • [13] Z. Olszak, On contact metric manifolds, Tohoku Math. J. (2), 31, 247–253, 1979.
  • [14] D. Perrone, Contact metric manifolds whose characteristic vector field is harmonic vector field, Differential Geom. Appl. 20, 367–378, 2004.
  • [15] T. Yamazaki, On a surgery of K-contact manifolds, Kodai Math. J. 24 (2), 214–225, 2001.
  • [16] T. Yamazaki, A construction of K-contact manifolds by a fiber join, Tohoku Math. J. (2), 51 (4), 433–446, 1999.
  • [17] A. Yildiz and E. Ata, On a type of K-contact manifolds, Hacet. J. Math. Stat. 41 (4), 567–571, 2012.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sharief Deshmukh 0000-0003-3700-8164

Amira Ishan This is me 0000-0002-1729-4805

Publication Date December 8, 2020
Published in Issue Year 2020 Volume: 49 Issue: 6

Cite

APA Deshmukh, S., & Ishan, A. (2020). A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics, 49(6), 2007-2016. https://doi.org/10.15672/hujms.551596
AMA Deshmukh S, Ishan A. A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics. December 2020;49(6):2007-2016. doi:10.15672/hujms.551596
Chicago Deshmukh, Sharief, and Amira Ishan. “A Note on Contact Metric Manifolds”. Hacettepe Journal of Mathematics and Statistics 49, no. 6 (December 2020): 2007-16. https://doi.org/10.15672/hujms.551596.
EndNote Deshmukh S, Ishan A (December 1, 2020) A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics 49 6 2007–2016.
IEEE S. Deshmukh and A. Ishan, “A note on contact metric manifolds”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, pp. 2007–2016, 2020, doi: 10.15672/hujms.551596.
ISNAD Deshmukh, Sharief - Ishan, Amira. “A Note on Contact Metric Manifolds”. Hacettepe Journal of Mathematics and Statistics 49/6 (December 2020), 2007-2016. https://doi.org/10.15672/hujms.551596.
JAMA Deshmukh S, Ishan A. A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics. 2020;49:2007–2016.
MLA Deshmukh, Sharief and Amira Ishan. “A Note on Contact Metric Manifolds”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, 2020, pp. 2007-16, doi:10.15672/hujms.551596.
Vancouver Deshmukh S, Ishan A. A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):2007-16.