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$\delta $-invariants; CR submanifolds; ideal submanifolds
An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
[1] Chen, B. Y.: CR-submanifolds of a Kähler manifold. I. J. Differ. Geom. 16 (1981), 305-322. MR 0638795 | Zbl 0431.53048
[2] Chen, B. Y.: CR-submanifolds of a Kähler manifold. II. J. Differ. Geom. 16 (1981), 493-509. MR 0654640
[3] Chen, B. Y.: Some new obstructions to minimal and Lagrangian isometric immersions. Jap. J. Math., New Ser. 26 (2000), 105-127. MR 1771434 | Zbl 1026.53009
[4] Chen, B. Y.: Pseudo-Riemannian Geometry, $\delta$-Invariants and Applications. World Scientific, Hackensack, NJ (2011). MR 2799371 | Zbl 1245.53001
[5] Chen, B. Y., Ludden, G. D., Montiel, S.: Real submanifolds of a Kähler manifold. Algebras Groups Geom. 1 (1984), 176-212. MR 0760492
[6] Djorić, M., Okumura, M.: CR Submanifolds of Complex Projective Space. Developments in Mathematics 19. Springer, Berlin (2010). DOI 10.1007/978-1-4419-0434-8_16 | MR 2566776 | Zbl 1187.32031
[7] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Differential Geometry and Its Applications (Eger, 1989) Colloq. Math. Soc. János Bolyai 56. North-Holland Amsterdam (1992), 573-585. MR 1211684
[8] Sasahara, T.: On Ricci curvature of CR-submanifolds wit rank one totally real distribution. Nihonkai Math. J. 12 (2001), 47-58. MR 1833741
[9] Sasahara, T.: On Chen invariant of CR-submanifolds in a complex hyperbolic space. Tsukuba J. Math. 26 (2002), 119-132. MR 1915981 | Zbl 1129.53302
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