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Title: A Frankel type theorem for CR submanifolds of Sasakian manifolds (English)
Author: Di Pinto, Dario
Author: Lotta, Antonio
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 59
Issue: 5
Year: 2023
Pages: 369-381
Summary lang: English
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Category: math
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Summary: We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms. (English)
Keyword: intersection of submanifolds
Keyword: CR submanifold of a Sasakian manifold
Keyword: scalar Levi form
MSC: 53C25
MSC: 53C40
idZBL: Zbl 07790553
idMR: MR4641952
DOI: 10.5817/AM2023-5-369
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Date available: 2023-08-15T13:35:26Z
Last updated: 2024-02-13
Stable URL: http://hdl.handle.net/10338.dmlcz/151793
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Reference: [1] Bejancu, A.: Geometry of CR-submanifolds.Mathematics and its Applications (East European Series), vol. 23, D. Reidel Publishing Co., Dordrecht, 1986. Zbl 0605.53001, MR 0861408
Reference: [2] Bejancu, A., Papaghiuc, N.: Semi-invariant submanifolds of a Sasakian manifold.An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27 (1981), 163–170. MR 0618723
Reference: [3] Binh, T.Q., Ornea, L., Tamássy, L.: Intersections of Riemannian submanifolds. Variations on a theme by T.J. Frankel.Rend. Mat. Appl. (7) 19 (1999), 107–121. MR 1710117
Reference: [4] Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds.second ed., Progress in Mathematics, vol. 203, Birkhäuser, Boston, 2010. Zbl 1246.53001, MR 2682326
Reference: [5] Djorić, M., Okumura, M.: CR submanifolds of complex projective space.Developments in Mathematics, vol. 19, Springer, New York, 2010. MR 2566776, 10.1007/978-1-4419-0434-8_16
Reference: [6] Falcitelli, M., Ianus, S., Pastore, A.M.: Riemannian submersions and related topics.World Scientific Publishing Co., Singapore, 2004. MR 2110043
Reference: [7] Frankel, T.: Manifolds with positive curvature.Pacific J. Math. 11 (1961), 165–171. MR 0123272, 10.2140/pjm.1961.11.165
Reference: [8] Goldberg, S.I., Kobayashi, S.: Holomorphic bisectional curvature.J. Differential Geom. 1 (1967), 225–233. MR 0227901, 10.4310/jdg/1214428090
Reference: [9] Medori, C., Nacinovich, M.: Levi-Tanaka algebras and homogeneous CR manifolds.Compositio Math. 109 (1997), 195–250. MR 1478818, 10.1023/A:1000166119593
Reference: [10] Pitis, G.: On the topology of Saskian manifolds.Math. Scand. 93 (2003), 99–108. MR 1997875, 10.7146/math.scand.a-14415
Reference: [11] Sakai, T.: Riemannian Geometry.Translations of Mathematical Monographs, vol. 149, Amer. Math. Soc., Providence, 1996. MR 1390760
Reference: [12] Takahashi, T.: Sasakian $\phi $-symmetric spaces.Tôhoku Math. J. 29 (1977), 91–113. MR 0440472, 10.2748/tmj/1178240699
Reference: [13] Tanno, S., Baik, S.-B.: $\phi $-holomorphic special bisectional curvature.Tôhoku Math. J. 22 (1970), 184–190. MR 0268829, 10.2748/tmj/1178242811
Reference: [14] Yano, K., Kon, M.: Generic submanifolds of Sasakian manifolds.Kodai Math. J. 3 (1980), 163–196. MR 0588453, 10.2996/kmj/1138036191
Reference: [15] Yano, K., Kon, M.: CR submanifolds of Kaehlerian and Sasakian manifolds.Progress in Mathematics, vol. 30, Birkhäuser, Boston, Mass., 1983. MR 0688816
Reference: [16] Yano, K., Kon, M.: Structures on Manifolds.Series in Pure Mathematics, vol. 3, World Scientific Publishing Co., Singapore, 1984. Zbl 0557.53001, MR 0794310
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