Araştırma Makalesi
Yıl 2020,
Cilt: 49 Sayı: 6, 2007 - 2016, 08.12.2020
Öz
Kaynakça
- [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.
Yıl 2020,
Cilt: 49 Sayı: 6, 2007 - 2016, 08.12.2020
Öz
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.
Anahtar Kelimeler
contact metric manifolds K-contact manifolds Killing vector field Sasakian manifolds
Kaynakça
- [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.
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 8 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 6 |