Geodesic
On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kählerian manifold
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 2, pp. 177-189 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose a fiber-wise deformation of the Sasaki metric on slashed and unit tangent bundles over the Kälerian manifold based on the Berger deformation of metric on a unit sphere. The geodesics of this metric have different projections on a base manifold for the slashed and unit tangent bundles in contrast to usual Sasaki metric. Nevertheless, the projections of geodesics of the unit tangent bundle over the locally symmetric Kählerian manifold still preserve the property to have all geodesic curvatures constant. 
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     author = {A. Yampolsky},
     title = {On geodesics of tangent bundle with fiberwise deformed {Sasaki} metric over {K\"ahlerian} manifold},
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A. Yampolsky. On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kählerian manifold. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 2, pp. 177-189. http://geodesic.mathdoc.fr/item/JMAG_2012_8_2_a4/

[1] S. Sasaki, “Geodesics on the Tangent Sphere Bundle over Space Forms”, J. Reine Angew. Math., 288 (1976), 106–120 | MR | Zbl

[2] K. Sato, “Geodesics on the Tangent Bundle over Space Forms”, Tensor, 32 (1978), 5–10 | MR | Zbl

[3] P.T. Nagy, “Geodesics on the Tangent Sphere Bundle of a Riemannian Manifold”, Geom. Dedic., 7:2 (1978), 233–244 | DOI | MR

[4] J. Cheeger and D. Gromoll, “On the Structure of Complete Manifolds of Nonnegative Curvature”, Ann. Math., 96 (1972), 413–443 | DOI | MR | Zbl

[5] M. Sekizawa, “Curvatures of Tangent Bundles with Cheeger–Gromoll Metric”, Tokyo J. Math., 14:2 (1991), 407–417 | DOI | MR | Zbl

[6] M.T.K. Abbassi and M. Sarih, “On Riemannian $g$-Natural Metrics of the Form $ag^s+ bg^h + cg^v $ on the Tangent Bundle of a Riemannian Manifold $(M, g)$”, Mediter. J. Math., 2 (2005), 19–43 | DOI | MR | Zbl

[7] V. Oproiu, “A Kähler Einstein Structure on the Tangent Bundle of a Space Form”, Int. J. Math. Math. Sci., 25 (2001), 183–195 | DOI | MR | Zbl

[8] M. Munteanu, Cheeger Gromoll Type Metrics on the Tangent Bundle, 2006, arXiv: math.DG/0610028 | MR

[9] O. Kowalski, “Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold”, J. Reine Angew. Math., 250 (1971), 124–129 | MR | Zbl

[10] J. Math. Sci., 69:1 (1994), 916–920 | DOI | MR