Next we also construct some almost anti-paraHermitian structures on T∗MT∗M and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler with respect to the Berger type deformed Sasaki metric.
📌 3 Key Takeaways
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Objective & Hypothesis:In the present paper, we study some notes on Berger type deformed Sasaki metric in the cotangent bundle T∗MT∗M over an anti-paraKähler manifold (M,φ,g)(M,φ,g).
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Key Findings & Data:We characterize some geodesic properties for this metric.
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Conclusion & Impact:Next we also construct some almost anti-paraHermitian structures on T∗MT∗M and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler with respect to the Berger type deformed Sasaki metric.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Horizontal lift and vertical lift · cotangent bundle · Berger type deformed Sasaki metric
Abstract
In the present paper, we study some notes on Berger type deformed Sasaki metric in the cotangent bundle T∗MT∗M over an anti-paraKähler manifold (M,φ,g)(M,φ,g). We characterize some geodesic properties for this metric. Next we also construct some almost anti-paraHermitian structures on T∗MT∗M and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler with respect to the Berger type deformed Sasaki metric.
ZAGANE, A. (2022). Some Notes on Berger Type Deformed Sasaki Metric in the Cotangent Bundle. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 348–360. https://ajindex.com/articles/539588
Ağca, F.: g-Natural Metrics on the cotangent bundle. Int. Electron. J. Geom. 6(1), 129-146 (2013)
Ağca, F., Salimov, A. A.: Some notes concerning Cheeger-Gromoll metrics. Hacet. J. Math. Stat. 42(5), 533-549 (2013)
Altunbas, M., Simsek, R., Gezer A.: A Study Concerning Berger type deformed Sasaki Metric on the Tangent Bundle. Zh. Mat. Fiz. Anal. Geom. 15(4), 435-447 (2019).
Cruceanu, V., Fortuny, P., Gadea, P. M.: A survey on paracomplex geometry. Rocky Mountain J. Math. 26(1), 83-115 (1996). doi:10.1216/rmjm/1181072105 [5] De León, M., Rodrigues, P. R. Methods of Differential Geometry in Analytical Mechanics. North-Holland Mathematics Studies, (1989).
Ganchev, G. T., Borisov, A. V.: Note on the almost complex manifolds with a Norden metric. C. R. Acad. Bulgarie Sci. 39(5), 31-34 (1986)
Gezer, A., Altunbas, M.: On the Rescaled Riemannian Metric of Cheeger Gromoll Type on the Cotangent Bundle. Hacet. J. Math. Stat. 45(2), 355-365 (2016). https:// Doi:10.15672/HJMS.20164515849 [8] Manev, M., Mekerov, D.: On Lie groups as quasi-Kähler manifolds with Killing Norden metric. Adv. Geom. 8(3), 343-352 (2008).
Ocak, F.: Notes About a New Metric on the Cotangent Bundle. Int. Electron. J. Geom. 12(2), 241-249 (2019).
Patterson, E. M., Walker, A. G.: Riemannian extensions. Quart. J.Math. Oxford Ser. 2(3), 19-28 (1952)
Salimov, A. A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterr. J. Math. 8(2), 243-255 (2011).
Salimov, A. A., Gezer, A., Iscan, M.: On anti-paraKähler structures on the tangent bundles. Ann. Polon. Math. 103(3), 247-261 (2012).
Salimov, A. A., Iscan, M., Akbulut, K.: Notes on para-Norden-Walker 4-manifolds. Int. J. Geom. Methods Mod. Phys. 7(8), 1331-1347 (2010).
Salimov, A. A., Iscan, M., Etayo, F.: Para-holomorphic B-manifold and its properties. Topology Appl. 154(4), 925-933 (2007).
Sekizawa, M.: Natural transformations of affine connections on manifolds to metrics on cotangent bundles. In: Proceedings of 14thWinter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14, 129-142 (1987)