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BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 2, 1256 - 1265, 31.12.2020
https://doi.org/10.31801/cfsuasmas.546701

Öz

Kaynakça

  • Geiges, H., A brief history of contact geometry and topology, Expositiones Mathematicae, 19(1) (2001), 25-53.
  • Kholodenko, A. L., Applications of contact geometry and topology in physics, World Scientific, (2013)
  • Yano, K., Concircular geometry I: concircular transformations, Proceedings of the Imperial Academy, 16(6) (1940), 195-200.
  • Yano, K., Sawaski, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geo,. 2 (1968), 161-184
  • De, U. C., Shaikh, A. A., Complex manifolds and contact manifolds, Narosa Publishing House, (2009).
  • Turgut Vanli, A., Unal, I., Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds. International Journal of Geometric Methods in Modern Physics, 14(05) (2017), 1750067.
  • Blair, D. E., Ludden, G. D., Yano, K., Geometry of complex manifolds similar to the Calabi-Eckmann manifolds, Journal of Differential Geometry, 9(2) (1974), 263-274.
  • Bande, G. and Hadjar, A., Contact pairs. Tohoku Mathematical Journal, Second Series, 57(2) (2005), 247-260.
  • Bande, G., Hadjar, A., On normal contact pairs, International Journal of Mathematics, 21(06) (2010), 737-754.
  • Bande, G., Hadjar, A., Contact pair structures and associated metrics, In Differential Geometry, (2009), 266-275
  • Bande, G., Blair, D. E., Hadjar, A., On the curvature of metric contact pairs, Mediterranean journal of mathematics, 10(2) (2013), 989-1009.
  • Bande, G., Blair, D. E., Hadjar, A., Bochner and conformal flatness of normal metric contact pairs, Annals of Global Analysis and Geometry, 48(1) (2015), 47-56.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Springer Science Business Media, (2010).
  • Kobayashi, S., Remarks on complex contact manifolds, Proc. Amer. Math. Soc., 10 (1959), 164-167.
  • Ishihara, S., Konishi, M., Complex almost contact structures in a complex contact manifold, Kodai Math. J., 5 (1982), 30--37
  • Korkmaz, B., Normality of complex contact manifolds, Rocky Mountain J. Math., 30 (2000), 1343-1380
  • Turgut Vanli, A., Blair, D. E., The Boothby-Wang Fibration of the Iwasawa Manifold as a Critical Point of the Energy, Monatsh. Math. 147 (2006), 75-84.
  • Bande, G., Hadjar, A., On the characteristic foliations of metric contact pairs, Harmonic Maps and Differential Geometry. Contemp. Math, 542 (2011), 255-259.
  • Beldjilali, G., Belkhelfa, M., Structures on the product of two almost Hermitian almost contact manifolds, International Electronic Journal of Geometry, 9(2) (2016), 80-86.

Some flatness conditions on normal metric contact pairs

Yıl 2020, Cilt: 69 Sayı: 2, 1256 - 1265, 31.12.2020
https://doi.org/10.31801/cfsuasmas.546701

Öz

In this paper, the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and has positive sectional curvature. It is also shown that a concircular flat normal metric contact pair manifold is an Einstein manifold. Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and, is a space of constant curvature.

Kaynakça

  • Geiges, H., A brief history of contact geometry and topology, Expositiones Mathematicae, 19(1) (2001), 25-53.
  • Kholodenko, A. L., Applications of contact geometry and topology in physics, World Scientific, (2013)
  • Yano, K., Concircular geometry I: concircular transformations, Proceedings of the Imperial Academy, 16(6) (1940), 195-200.
  • Yano, K., Sawaski, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geo,. 2 (1968), 161-184
  • De, U. C., Shaikh, A. A., Complex manifolds and contact manifolds, Narosa Publishing House, (2009).
  • Turgut Vanli, A., Unal, I., Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds. International Journal of Geometric Methods in Modern Physics, 14(05) (2017), 1750067.
  • Blair, D. E., Ludden, G. D., Yano, K., Geometry of complex manifolds similar to the Calabi-Eckmann manifolds, Journal of Differential Geometry, 9(2) (1974), 263-274.
  • Bande, G. and Hadjar, A., Contact pairs. Tohoku Mathematical Journal, Second Series, 57(2) (2005), 247-260.
  • Bande, G., Hadjar, A., On normal contact pairs, International Journal of Mathematics, 21(06) (2010), 737-754.
  • Bande, G., Hadjar, A., Contact pair structures and associated metrics, In Differential Geometry, (2009), 266-275
  • Bande, G., Blair, D. E., Hadjar, A., On the curvature of metric contact pairs, Mediterranean journal of mathematics, 10(2) (2013), 989-1009.
  • Bande, G., Blair, D. E., Hadjar, A., Bochner and conformal flatness of normal metric contact pairs, Annals of Global Analysis and Geometry, 48(1) (2015), 47-56.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Springer Science Business Media, (2010).
  • Kobayashi, S., Remarks on complex contact manifolds, Proc. Amer. Math. Soc., 10 (1959), 164-167.
  • Ishihara, S., Konishi, M., Complex almost contact structures in a complex contact manifold, Kodai Math. J., 5 (1982), 30--37
  • Korkmaz, B., Normality of complex contact manifolds, Rocky Mountain J. Math., 30 (2000), 1343-1380
  • Turgut Vanli, A., Blair, D. E., The Boothby-Wang Fibration of the Iwasawa Manifold as a Critical Point of the Energy, Monatsh. Math. 147 (2006), 75-84.
  • Bande, G., Hadjar, A., On the characteristic foliations of metric contact pairs, Harmonic Maps and Differential Geometry. Contemp. Math, 542 (2011), 255-259.
  • Beldjilali, G., Belkhelfa, M., Structures on the product of two almost Hermitian almost contact manifolds, International Electronic Journal of Geometry, 9(2) (2016), 80-86.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

İnan Ünal 0000-0003-1318-9685

Yayımlanma Tarihi 31 Aralık 2020
Gönderilme Tarihi 29 Mart 2019
Kabul Tarihi 20 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 2

Kaynak Göster

APA Ünal, İ. (2020). Some flatness conditions on normal metric contact pairs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1256-1265. https://doi.org/10.31801/cfsuasmas.546701
AMA Ünal İ. Some flatness conditions on normal metric contact pairs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2020;69(2):1256-1265. doi:10.31801/cfsuasmas.546701
Chicago Ünal, İnan. “Some Flatness Conditions on Normal Metric Contact Pairs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 2 (Aralık 2020): 1256-65. https://doi.org/10.31801/cfsuasmas.546701.
EndNote Ünal İ (01 Aralık 2020) Some flatness conditions on normal metric contact pairs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1256–1265.
IEEE İ. Ünal, “Some flatness conditions on normal metric contact pairs”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 2, ss. 1256–1265, 2020, doi: 10.31801/cfsuasmas.546701.
ISNAD Ünal, İnan. “Some Flatness Conditions on Normal Metric Contact Pairs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (Aralık 2020), 1256-1265. https://doi.org/10.31801/cfsuasmas.546701.
JAMA Ünal İ. Some flatness conditions on normal metric contact pairs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1256–1265.
MLA Ünal, İnan. “Some Flatness Conditions on Normal Metric Contact Pairs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 2, 2020, ss. 1256-65, doi:10.31801/cfsuasmas.546701.
Vancouver Ünal İ. Some flatness conditions on normal metric contact pairs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1256-65.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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