Araştırma Makalesi
Yıl 2021,
Sayı: 34, 115 - 122, 30.03.2021
Öz
Kaynakça
- D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Springer Science Business Media, 2010.
- S. Kobayashi, Remarks on Complex Contact Manifolds, Proceedings of the American Mathematical Society 10 (1959) 164-167.
- S. Ishihara, M. Konishi, Complex Almost-contact Structures in a Complex Contact Manifold, Kodai Mathematical Journal 5 (1982) 30-37.
- B. Korkmaz, Normality of Complex Contact Manifolds, Rocky Mountain Journal of Mathematics 30 (2000) 1343-1380.
- A. T. Vanlı, D. E. Blair, The Boothby-Wang Fibration of the Iwasawa Manifold as a Critical Point of the Energy, Monatshefte für Mathematik 147 (2006) 75-84.
- A. T. Vanlı, İ. Ünal, Conformal, Concircular, Quasi-conformal and Conharmonic Flatness on Normal Complex Contact Metric Manifolds, International Journal of Geometric Methods in Modern Physics 14(05) (2017). doi: 10.1142/S0219887817500670
- A. T. Vanlı, İ. Ünal, I. On Complex \eta-Einstein Normal Complex Contact Metric Manifolds, Communications in Mathematics and Application 8(3) (2017) 301-313. doi:10.26713/cma.v8i3.509
- D. Fetcu, Harmonic Maps between Complex Sasakian Manifolds, Rendiconti del Seminario Matematico Universita e Politecnico di Torino 64 (2006) 319-329.
- B. J. Foreman, Complex Contact Manifolds and Hyperkahler Geometry, Kodai Mathematical Journal 23(1) (2000) 12-26.
- D. Fetcu, An Adapted Connection on a Strict Complex Contact Manifold, in Proceedings of the 5th Conference of Balkan Society of Geometers (2006) 54-61.
- A. T. Vanlı, İ. Ünal, K. Avcu, On Complex Sasakian Manifolds, Afrika Matematika (2020) 1-10.
- E. Calabi, B. Eckmann, A Class of Compact Complex Manifolds Which are Not Algebraic, Annals of Mathematics 58 (1953) 494-500.
- D. E. Blair, G. D. Ludden, K. Yano, Geometry of Complex Manifolds Similar to the Calabi-Eckmann Manifolds, Journal of Differential Geometry 9(2) (1974) 263-274.
- K. Abe, On a Class of Hermitian Manifolds, Inventiones Mathematicae 51(2) (1979) 103-121.
- G. Bande, A. Hadjar, Contact Pairs, Tohoku Mathematical Journal 57(2) (2005) 247-260. doi:10.2748/tmj/1119888338
- G. Bande, A. Hadjar, Contact Pair Structures and Associated Metrics, Differential Geometry-Proceedings of the $ VIII $ International Colloquium (2009) 266-275.
- G. Bande, A. Hadjar, On Normal Contact Pairs, International Journal of Mathematics 21(06) (2010) 737-754. doi: 10.1142/S0129167X10006197
- G. Bande, D. E. Blair, A. Hadjar, Bochner and Conformal Flatness of Normal Metric Contact Pairs, Annals of Global Analysis and Geometry 48(1) (2015) 47-56.
- G. Bande, A. Hadjar, On the Characteristic Foliations of Metric Contact Pairs, Harmonic Maps and Differential Geometry, Contemporary Mathematics 542 (2011) 255-259.
- G. Bande, D. E. Blair, A. Hadjar, On the Curvature of Metric Contact Pairs, Mediterranean Journal of Mathematics 10(2) (2013) 989-1009.
- İ. Ünal, Generalized Quasi-Einstein Manifolds in Contact Geometry, Mathematics 8(9) (2020) 1-14.
- İ. Ünal, Some Flatness Conditions on Normal Metric Contact Pairs, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69(2) (2020) 262-271.
- İ. Ünal, On Metric Contact Pairs with Certain Semi-symmetry Conditions, Journal of Polytechnic 24(1) (2021) 333-338.
- İ. Ünal, Generalized Quasi-Conformal Curvature Tensor on Normal Metric Contact Pairs, International Journal of Pure and Applied Sciences 6(2) (2020) 194-199.
- U. C. De, S. Mallick, On Generalized Quasi-Einstein Manifolds Admitting Certain Vector Fields, Filomat 29(3) (2015) 599-609.
- D. G. Prakasha, H. Venkatesha Some Results on Generalized Quasi-Einstein Manifolds, Chinese Journal of Mathematics Article ID 563803 (2014) 5 pages.
- M. C. Chaki On Pseudo Ricci Symmetric Manifolds, Bulgarian Journal of Physics 15(6) (1988) 526-531.
- B. Kirik, Generalized Quasi-Einstein Manifolds Admitting Special Vector Fields, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 31(1) (2015) 61-69.
- R. Hamilton, The Ricci flow on Surfaces, Contemporary Mathematics 71 (1988) 237-261.
- G. Ayar, M. Yıldırım, Ricci Solitons and Gradient Ricci Solitons on Nearly Kenmotsu Manifolds, Facta Universitatis, Series: Mathematics and Informatics 34(3) (2019) 503-510.
- C. S. Bagewadi, G. Ingalahalli, S. R. Ashoka, A Study on Ricci Solitons in Kenmotsu Manifolds, International Scholarly Research Notices Geometry Article ID 412593 (2013) 6 pages.
- G. Ayar, D. Demirhan, Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection, Journal of Engineering Technology and Applied Sciences 4(3) (2019) 131-140. doi:10.30931/jetas.643643
- H. İ. Yoldaş, E. Yaşar On Submanifolds of Kenmotsu Manifold with Torqued Vector Field, Hacettepe Journal of Mathematics and Statistics 49(2) (2020) 843-853.
Yıl 2021,
Sayı: 34, 115 - 122, 30.03.2021
Öz
In this study, we work on normal-metric contact pair manifolds under certain conditions related to the Ricci curvature. We obtain some results for generalized quasi-Einstein normal-metric contact pair manifolds. We prove that such manifolds are not pseudo-Ricci symmetric. Finally, we investigate Ricci solitons on normal-metric contact pair manifolds.
Anahtar Kelimeler
Ricci symmetric Normal-metric contact pair manifold generalized quasi-Einstein Ricci curvature
Kaynakça
- D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Springer Science Business Media, 2010.
- S. Kobayashi, Remarks on Complex Contact Manifolds, Proceedings of the American Mathematical Society 10 (1959) 164-167.
- S. Ishihara, M. Konishi, Complex Almost-contact Structures in a Complex Contact Manifold, Kodai Mathematical Journal 5 (1982) 30-37.
- B. Korkmaz, Normality of Complex Contact Manifolds, Rocky Mountain Journal of Mathematics 30 (2000) 1343-1380.
- A. T. Vanlı, D. E. Blair, The Boothby-Wang Fibration of the Iwasawa Manifold as a Critical Point of the Energy, Monatshefte für Mathematik 147 (2006) 75-84.
- A. T. Vanlı, İ. Ünal, Conformal, Concircular, Quasi-conformal and Conharmonic Flatness on Normal Complex Contact Metric Manifolds, International Journal of Geometric Methods in Modern Physics 14(05) (2017). doi: 10.1142/S0219887817500670
- A. T. Vanlı, İ. Ünal, I. On Complex \eta-Einstein Normal Complex Contact Metric Manifolds, Communications in Mathematics and Application 8(3) (2017) 301-313. doi:10.26713/cma.v8i3.509
- D. Fetcu, Harmonic Maps between Complex Sasakian Manifolds, Rendiconti del Seminario Matematico Universita e Politecnico di Torino 64 (2006) 319-329.
- B. J. Foreman, Complex Contact Manifolds and Hyperkahler Geometry, Kodai Mathematical Journal 23(1) (2000) 12-26.
- D. Fetcu, An Adapted Connection on a Strict Complex Contact Manifold, in Proceedings of the 5th Conference of Balkan Society of Geometers (2006) 54-61.
- A. T. Vanlı, İ. Ünal, K. Avcu, On Complex Sasakian Manifolds, Afrika Matematika (2020) 1-10.
- E. Calabi, B. Eckmann, A Class of Compact Complex Manifolds Which are Not Algebraic, Annals of Mathematics 58 (1953) 494-500.
- D. E. Blair, G. D. Ludden, K. Yano, Geometry of Complex Manifolds Similar to the Calabi-Eckmann Manifolds, Journal of Differential Geometry 9(2) (1974) 263-274.
- K. Abe, On a Class of Hermitian Manifolds, Inventiones Mathematicae 51(2) (1979) 103-121.
- G. Bande, A. Hadjar, Contact Pairs, Tohoku Mathematical Journal 57(2) (2005) 247-260. doi:10.2748/tmj/1119888338
- G. Bande, A. Hadjar, Contact Pair Structures and Associated Metrics, Differential Geometry-Proceedings of the $ VIII $ International Colloquium (2009) 266-275.
- G. Bande, A. Hadjar, On Normal Contact Pairs, International Journal of Mathematics 21(06) (2010) 737-754. doi: 10.1142/S0129167X10006197
- G. Bande, D. E. Blair, A. Hadjar, Bochner and Conformal Flatness of Normal Metric Contact Pairs, Annals of Global Analysis and Geometry 48(1) (2015) 47-56.
- G. Bande, A. Hadjar, On the Characteristic Foliations of Metric Contact Pairs, Harmonic Maps and Differential Geometry, Contemporary Mathematics 542 (2011) 255-259.
- G. Bande, D. E. Blair, A. Hadjar, On the Curvature of Metric Contact Pairs, Mediterranean Journal of Mathematics 10(2) (2013) 989-1009.
- İ. Ünal, Generalized Quasi-Einstein Manifolds in Contact Geometry, Mathematics 8(9) (2020) 1-14.
- İ. Ünal, Some Flatness Conditions on Normal Metric Contact Pairs, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69(2) (2020) 262-271.
- İ. Ünal, On Metric Contact Pairs with Certain Semi-symmetry Conditions, Journal of Polytechnic 24(1) (2021) 333-338.
- İ. Ünal, Generalized Quasi-Conformal Curvature Tensor on Normal Metric Contact Pairs, International Journal of Pure and Applied Sciences 6(2) (2020) 194-199.
- U. C. De, S. Mallick, On Generalized Quasi-Einstein Manifolds Admitting Certain Vector Fields, Filomat 29(3) (2015) 599-609.
- D. G. Prakasha, H. Venkatesha Some Results on Generalized Quasi-Einstein Manifolds, Chinese Journal of Mathematics Article ID 563803 (2014) 5 pages.
- M. C. Chaki On Pseudo Ricci Symmetric Manifolds, Bulgarian Journal of Physics 15(6) (1988) 526-531.
- B. Kirik, Generalized Quasi-Einstein Manifolds Admitting Special Vector Fields, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 31(1) (2015) 61-69.
- R. Hamilton, The Ricci flow on Surfaces, Contemporary Mathematics 71 (1988) 237-261.
- G. Ayar, M. Yıldırım, Ricci Solitons and Gradient Ricci Solitons on Nearly Kenmotsu Manifolds, Facta Universitatis, Series: Mathematics and Informatics 34(3) (2019) 503-510.
- C. S. Bagewadi, G. Ingalahalli, S. R. Ashoka, A Study on Ricci Solitons in Kenmotsu Manifolds, International Scholarly Research Notices Geometry Article ID 412593 (2013) 6 pages.
- G. Ayar, D. Demirhan, Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection, Journal of Engineering Technology and Applied Sciences 4(3) (2019) 131-140. doi:10.30931/jetas.643643
- H. İ. Yoldaş, E. Yaşar On Submanifolds of Kenmotsu Manifold with Torqued Vector Field, Hacettepe Journal of Mathematics and Statistics 49(2) (2020) 843-853.
Toplam 33 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Mart 2021 |
| Gönderilme Tarihi | 22 Mart 2021 |
| Yayımlandığı Sayı | Yıl 2021 Sayı: 34 |
Kaynak Göster
- Makale Dosyaları