Research Article
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Year 2021, Issue: 34, 115 - 122, 30.03.2021

Abstract

References

  • 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.

On the Ricci Curvature of Normal-Metric Contact Pair Manifolds

Year 2021, Issue: 34, 115 - 122, 30.03.2021

Abstract

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.

References

  • 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.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

İnan Ünal 0000-0003-1318-9685

Ramazan Sarı 0000-0002-4618-8243

Publication Date March 30, 2021
Submission Date March 22, 2021
Published in Issue Year 2021 Issue: 34

Cite

APA Ünal, İ., & Sarı, R. (2021). On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. Journal of New Theory(34), 115-122.
AMA Ünal İ, Sarı R. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT. March 2021;(34):115-122.
Chicago Ünal, İnan, and Ramazan Sarı. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory, no. 34 (March 2021): 115-22.
EndNote Ünal İ, Sarı R (March 1, 2021) On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. Journal of New Theory 34 115–122.
IEEE İ. Ünal and R. Sarı, “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”, JNT, no. 34, pp. 115–122, March 2021.
ISNAD Ünal, İnan - Sarı, Ramazan. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory 34 (March 2021), 115-122.
JAMA Ünal İ, Sarı R. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT. 2021;:115–122.
MLA Ünal, İnan and Ramazan Sarı. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory, no. 34, 2021, pp. 115-22.
Vancouver Ünal İ, Sarı R. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT. 2021(34):115-22.


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