| Title: | Geometry of Mus-Sasaki metric (English) | 
| Author: | Zagane, Abderrahim | 
| Author: | Djaa, Mustapha | 
| Language: | English | 
| Journal: | Communications in Mathematics | 
| ISSN: | 1804-1388 | 
| Volume: | 26 | 
| Issue: | 2 | 
| Year: | 2018 | 
| Pages: | 113-126 | 
| Summary lang: | English | 
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| Category: | math | 
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| Summary: | In this paper, we introduce the Mus-Sasaki metric on the tangent bundle $TM$ as a new natural metric non-rigid on $TM$. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature. (English) | 
| Keyword: | Horizontal lift | 
| Keyword: | vertical lift | 
| Keyword: | Mus-Sasaki metric | 
| Keyword: | scalar curvature. | 
| MSC: | 53A45 | 
| MSC: | 53C20 | 
| MSC: | 58E20 | 
| idZBL: | Zbl 07058959 | 
| idMR: | MR3898197 | 
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| Date available: | 2019-05-07T09:22:44Z | 
| Last updated: | 2020-01-05 | 
| Stable URL: | http://hdl.handle.net/10338.dmlcz/147658 | 
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| Reference: | [1] Abbassi, M.T.K., Sarih, M.: On Natural Metrics on Tangent Bundles of Riemannian Manifolds.Archivum Mathematicum, 41, 2005, 71-92,  MR 2142144 | 
| Reference: | [2] Cengiz, N., Salimov, A.A.: Diagonal lift in the tensor bundle and its applications.Appl. Math. Comput., 142, 2--3, 2003, 309-319,  MR 1979438 | 
| Reference: | [3] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature.Ann. of Math., 96, 2, 1972, 413-443,  Zbl 0246.53049, MR 0309010, 10.2307/1970819 | 
| Reference: | [4] Djaa, M., Djaa, N.E.H., Nasri, R.: Natural Metrics on $T^{2}M$ and Harmonicity.International Electronic Journal of Geometry, 6, 1, 2013, 100-111,  MR 3048524 | 
| Reference: | [5] Djaa, M., Gancarzewicz, J.: The geometry of tangent bundles of order r.Boletin Academia, Galega de Ciencias, 4, 1985, 147-165,  MR 0908354 | 
| Reference: | [6] Djaa, N.E.H., Ouakkas, S., Djaa, M.: Harmonic sections on the tangent bundle of order two.Annales Mathematicae et Informaticae, 38, 2011, 15-25,  MR 2872181 | 
| Reference: | [7] Dombrowski, P.: On the Geometry of the Tangent Bundle.J. Reine Angew. Math., 210, 1962, 73-88,  MR 0141050 | 
| Reference: | [8] Gezer, A.: On the Tangent Bundle With Deformed Sasaki Metric.International Electronic Journal of Geometry, 6, 2, 2013, 19-31,  MR 3125828 | 
| Reference: | [9] Gudmundsson, S., Kappos, E.: On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric.Tokyo J. Math., 25, 1, 2002, 75-83,  MR 1908215, 10.3836/tjm/1244208938 | 
| Reference: | [10] Sekizawa, O. Kowalski and M.: On Riemannian Geometry Of Tangent Sphere Bundles With Arbitrary Constant Radius.Archivum Mathematicum, 44, 2008, 391-401,  MR 2501575 | 
| Reference: | [11] Musso, E., Tricerri, F.: Riemannian Metrics on Tangent Bundles.Ann. Mat. Pura Appl., 150, 4, 1988, 1-19,  MR 0946027, 10.1007/BF01761461 | 
| Reference: | [12] Salimov, A.A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles.Mediterranean Journal of Mathematics, 8, 2, 2011, 243-255,  MR 2802327 | 
| Reference: | [13] Salimov, A.A, Gezer, A.: On the geometry of the $(1, 1$)-tensor bundle with Sasaki type metric.Chinese Annals of Mathematics, 32, 3, 2011, 369-386,  MR 2805406, 10.1007/s11401-011-0646-3 | 
| Reference: | [14] Salimov, A.A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles.Mediterr. J. Math, 6, 2, 2009, 135-147,  MR 2516246, 10.1007/s00009-009-0001-z | 
| Reference: | [15] Salimov, A.A., Kazimova, S.: Geodesics of the Cheeger-Gromoll Metric.Turk. J. Math., 33, 2009, 99-105,  MR 2524119 | 
| Reference: | [16] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds II.Tohoku Math. J., 14, 1962, 146-155,  MR 0145456, 10.2748/tmj/1178244169 | 
| Reference: | [17] Sekizawa, M.: Curvatures of Tangent Bundles with Cheeger-Gromoll Metric.Tokyo J. Math., 14, 2, 1991, 407-417,  MR 1138176, 10.3836/tjm/1270130381 | 
| Reference: | [18] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles.1973, Marcel Dekker. INC., New York,  Zbl 0262.53024, MR 0350650 | 
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