J-trajectories in Locally Conformal Kahler Manifolds with Parallel Anti Lee Field

Year 2020, Volume: 13 Issue: 2, 30 - 44, 15.10.2020

Jun-ichi Inoguchı

https://doi.org/10.36890/iejg.718806

Cited By: 10

Abstract

We show that J-trajectories in a locally conformal Kahler manifold with parallel anti Lee field are of osculating order at most 3.xxcbxcb xcbxcbxbcxbxcbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbxcvxvbvxbxcvbcxbvcxbvbsdbsdgndsb vsbsgbsgbsbvc bsbsgnsgdbsdgfnsgnsgdfbsfgbgnsgfgnsgfnhnffgsnbnsfgnsfgnsf bsgnsfnsfhnhngbsgbnsgfnbsgbsgfnsfgnb bxbxxbcbxbvxcbxcb lk<bc kşbckb kxzb kzkşşkzxv kzvxk kzv khzxvk  şofnvpoasfhovuhqw8qr891jğırbv*0invlqfbvkjffvlsdvnqjnfjvbjasknvoanpıufhbvoqnfbov  fğovhoqfbvnıqbfuvgşunbvşasbvoiqbpıyvbqiownvblisdmdvşklnasşkfbvjqfebşı qbefogs,fvmnğiqofbvkşqbfvljqnşfıvbqıfvbijqkbfvljikqbvljbsqkjvbqfhbvıqfbvşqbfvihqfbvşıhqebif,pıvbqşıbfv

Keywords

J-trajectory , LCK manifold , Kenmotsu manifold , magnetic curve

References

• [1] Adachi, T., Maeda, S.: Global behaviors of circles in a complex hyperbolic space. Tsukuba J. Math. 21 (1), 29-42 (1997). https://projecteuclid.org/euclid.tkbjm/1496163159
• [2] Adachi, T., Maeda, S., Udagawa, S.: Circles in a complex projective space. Osaka J. Math. 32, 709-719 (1995). https://projecteuclid.org/euclid.ojm/1200786276
• [3] Adachi, T., Maeda, S., Udagawa, S.: circles in compact Hermitian symmetric spaces. Tsukuba J. Math. 24 (1), 1-13 (2000). https://projecteuclid.org/euclid.tkbjm/1496164041
• [4] Adachi, T., Maeda, S., Udagawa, S.: Geometry of ordinary helices in a complex projective space. Hokkaido Math. J. 33 (1), 233-246 (2004). https://projecteuclid.org/euclid.hokmj/1285766002
• [5] de Andrés, L. C., Cordero, L. A., Fernández, M., Mencía, J. J.: Examples of four-dimensional compact locally conformal Kähler solvmanifolds. Geom. Dedicata 29 227-232 (1989). https://doi.org/10.1007/BF00182123
• [6] Ate¸s, C., Munteanu, M. I., Nistor, A. I.: Periodic J-trajectories on $\mathbb{R}\times\mathbb{S}^3$ J. Geom. Phys. 133, 141-152 (2018). https://doi.org/10.1016/j.geomphys.2018.07.002
• [7] Bratu, G.: Sur les équations intégrales non linéaires. Bull. Soc. Math. France 42 113-142 (1914). https://doi.org/10.24033/bsmf.943
• [8] Calin, C., Crasmareanu, C. M., Munteanu, M. I.: Slant curves in three-dimensional f-Kenmotsu manifolds. J. Math. Anal. Appl. 394 400-407 (2012). https://doi.org/10.1016/j.jmaa.2012.04.031
• [9] Dragomir, S., Ornea, L.: Locally Conformal Kähler Geometry, Progress in Mathematics. Birkhäuser Verlag, Basel, (1998).
• [10] Filipkiewicz, R.: Four dimensional geometries. Ph. D. thesis. University of Warwick (1983).
• [11] Frank-Kamenetskii D. A.: Diffusion and Heat Exchange in Chemical Kinetics. Princeton University Press. Princeton (1955).
• [12] Gelfand, I. M.: Some problems in the theory of quasilinear equations. In: Twelve papers on logic and differential equations. Amer. Math. Soc. Transl. 29 (2), 295-381, (1963).
• [13] Guest, M. A.: Harmonic Maps, Loop Groups and Integrable Systems. London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1997.
• [14] Inoguchi, J., Lee, J.-E.: Slant curves in 3-dimensional almost f-Kenmotsu manifolds. Comm. Korean Math. Soc. 32 (2) 417-424 (2017). https://doi.org/10.4134/CKMS.c160079
• [15] Inoguchi, J., Lee, J.-E.: J-trajectories in Vaisman manifolds. submitted.
• [16] Kamishima, Y.: Note on locally conformal Kähler surfaces. Geom. Dedicata 84 115-124 (2001). https://doi.org/10.1023/A:1010353217999
• [17] Kashiwada, T.: On a class of locally conformal Kähler manifolds. Tensor New Series 63 297-306 (2002).
• [18] Kasuya, H.: Vaisman metrics on solvmanifolds and Oeljeklaus–Toma manifolds. Bull. London Math. Soc. 45 (1) 15-26 (2013). https://doi.org/10.1112/blms/bds057
• [19] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Math. J. 24 93-103 (1972). https://projecteuclid.org/euclid.tmj/1178241594
• [20] Maeda, S., Adachi, T.: Holomorphic helices in a complex space form. Proc. Amer. Math. Soc. 125 (4) 1197-1202 (1997). https://doi.org/10.1090/S0002-9939-97-03627-7
• [21] Oeljeklaus, K., Toma, M.: Non-Kähler compact complex manifolds associated to number fields. Ann. Inst. Fourier (Grenoble) 55 (1) 161-171 (2005). https://doi.org/10.5802/aif.2093
• [22] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. London (1983).
• [23] Ornea, L.: Locally conformally Kähler manifolds. A selection of results. Lecture notes of Seminario Interdisciplinare di Matematica 4 121–152 (2005). (arXiv:math/0411503v2[math.DG]).
• [24] Pandey, P. K., Mohammad, S.: Magnetic and slant curves in Kenmotsu manifolds. Surveys in Mathematics and its Applications 15 139-151 (2020).
• [25] Rogers, C., Shardwick, W. R.: Bäcklund transformations and their applications. Academic Press. London (1982).
• [26] Sawai, H.: A construction of lattices on certain solvable Lie groups. Topology Appl. 154 3125-3134 (2007). https://doi.org/10.1016/j.topol.2007.08.006
• [27] Tricerri, F.: Some examples of locally conformal Kähler manifolds. Rendiconti del Seminario Matematico Università e Politecnico di Torino 40 81-92 (1982).
• [28] Vaisman, I.: On locally conformal almost Kähler manifolds. Israel J. Math. 24 338-351 (1976). https://doi.org/10.1007/BF02834764
• [29] Vaisman, I.: Locally conformal Kähler manifolds with parallel Lee form. Rendiconti di Matematica (6) 12 (2) 263-284 (1979).
• [30] Wall, C. T.: Geometric structures on compact complex analytic surfaces. Topology 25 (2) 119-153 (1986). https://doi.org/10.1016/0040- 9383(86)90035-2