Acta mathematica scientia, Series B >
NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE
Received date: 2012-09-17
Online published: 2014-01-20
Let (M, g) be an n-dimensional Riemannian manifold and T*M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T*M. Second, we construct locally decomposable Golden Riemannian structures on T*M. Finally we investigate curvature properties of T*M.
Aydin GEZER , Murat ALTUNBAS . NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 162 -174 . DOI: 10.1016/S0252-9602(13)60133-2
[1] Akbulut S, ¨Ozdemir M, Salimov A A. Diagonal lift in the cotangent bundle and its applications. Turkish J Math, 2001, 25(4): 491–502
[2] Crasmareanu M, Hretcanu C. Golden differential geometry. Chaos Solitons Fractals, 2008, 38(5): 1229–1238
[3] Cruceanu V, Fortuny P, Gadea P M. A survey on paracomplex Geometry. Rocky Mountain J Math, 1995, 26: 83–115
[4] Cruceanu V. Une classe de structures g´eom´e triques sur le fibr´e cotangent. Tensor (NS), 1993, 53: 196–201
[5] Drut¸?a L S. Classes of general natural almost anti-Hermitian structures on the cotangent bundles. Mediterr J Math, 2011, 8(2): 161–179
[6] Drut¸?a L S. Cotangent bundles with general natural K¨ahler structures of quasi-constant holomorphic sectional
curvatures//Differential Geometry. Hackensack, NJ: World Sci Publ, 2009: 311–315
[7] Drut¸?a L S. K¨ahler-Einstein structures of general natural lifted type on the cotangent bundles. Balkan J Geom Appl, 2009, 14(1): 30–39
[8] Drut¸?a L S. Cotangent bundles with general natural K¨ahler structures. Rev Roumaine Math Pures Appl, 2009, 54(1): 13–23
[9] Gezer A, Cengiz N, Salimov A A. On integrability of Golden Riemannian structures. Turk J Math, 2013, 37(4): 693–703
[10] Goldberg S I, Yano K. Polynomial structures on manifolds. Kodai Math Sem Rep, 1970, 22: 199–218
[11] Goldberg S I, Petridis N C. Differentiable solutions of algebraic equations on manifolds. Kodai Math Sem Rep, 1973, 25: 111–128
[12] Hretcanu C, Crasmareanu M. On some invariant submanifolds in a Riemannian manifold with Golden structure. An Stiins Univ Al I Cuza Iasi Mat (NS), 2007, 53(1): 199–211
[13] Hretcanu C, Crasmareanu M. Applications of the Golden ratio on Riemannian manifolds. Turkish J Math, 2009, 33(2): 179–191
[14] Kruchkovich G I. Hypercomplex structure on manifold, I. Tr Sem Vect Tens Anal Moscow Univ, 1972, 16: 174–201
[15] Marek-Crnjac L. The Golden mean in the topology of four-manifolds in conformal field theory in the mathematical probability theory and in Cantorian spacetime. Chaos Solitons & Fractals, 2006, 28(5): 1113–1118
[16] Marek-Crnjac L. Periodic continued fraction representations of different quarks mass ratios. Chaos, Solitons & Fractals, 2005, 25: 807–814
[17] Mok K P. Metrics and connections on the cotangent bundle. K¯odai Math Sem Rep, 1976/77, 28(2/3): 226–238
[18] Oproiu V, Poro¸sniuc D D. A class of K¨ahler Einstein structures on the cotangent bundle. Publ Math Debrecen, 2005, 66(3/4): 457–478
[19] Oproiu V, Poro¸sniuc D D. A K¨ahler Einstein structure on the cotangent bundle of a Riemannian manifold. An S¸tiint¸ Univ Al I Cuza Ia¸si Mat (NS), 2003, 49(2): 399–414
[20] Oproiu V, Papaghiuc N. On the cotangent bundle of a differentiable manifold. Publ Math Debrecen, 1997, 50(3/4): 317–338
[21] Oproiu V, Papaghiuc N, Mitric G. Some classes of para-Hermitian structures on cotangent bundles. An S¸tiint¸ Univ Al I Cuza Ia¸si Mat (NS), 1997, 43(1): 7–22
[22] Salimov A A, Agca F. Some properties of Sasakian metrics in cotangent bundles. Mediterr J Math, 2011, 8(2): 243–255
[23] Salimov A A, Iscan M, Etayo F. Paraholomorphic B-manifold and its properties. Topology Appl, 2007, 154(4): 925–933
[24] Sasaki S. On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math J, 1958, 10: 338–358
[25] Satˆo I. Complete lifts from a manifold to its cotangent bundle. K¯odai Math Sem Rep, 1968, 20: 458–468
[26] Di L, Sigalotti G, Mejias A. The Goldenratio in special relativity. Chaos, Solitons & Fractals, 2006, 30: 521–524
[27] Tachibana S. Analytic tensor and its generalization. Tohoku Math J, 1960, 12(2): 208–221
[28] Vishnevskii V V. Integrable affinor structures and their plural interpretations. J of Math Sciences, 2002, 108(2): 151–187
[29] Vishnevskii V V, Shirokov A P, Shurygin V V. Spaces Over Algebras. Kazan: Kazan Gos University, 1985(Russian)
[30] Wang J, Wang Y. On the geometry of tangent bundles with the rescaled metric. arXiv:1104.5584v1
[31] Yano K. On a structure defined by a tensor field f of type (1, 1) satisfying f3 +f = 0. Tensor (NS), 1963, 14: 99–109
[32] Yano K, Ako M. On certain operators associated with tensor field. Kodai Math Sem Rep, 1968, 20: 414–436
[33] Yano K, Ishihara S. Tangent and Cotangent Bundles. New York: Marcel Dekker Inc, 1973
[34] Zayatuev B V. On Geometry of Tangent Hermtian Surface. Webs and Quasigroups TSU, 1995: 139–143
[35] Zayatuev B V. On some clases of AH-structures on tangent bundles//Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], 2000: 53–54
[36] Zayatuev B V. On Some Classes of Almost-Hermitian Structures on the Tangent Bundle. Webs and Quasigroups TSU, 2002: 103–106
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