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Keywords:
quaternionic projective space; quaternionic number space; $QR$-submanifold; normal almost contact $3$-structure
quaternionic projective space; quaternionic number space; $QR$-submanifold; normal almost contact $3$-structure
Summary:
We study $n$-dimensional $QR$-submanifolds of $QR$-dimension $(p-1)$ immersed in a quaternionic space form $QP^{(n+p)/4}(c)$, $c\geqq 0$, and, in particular, determine such submanifolds with the induced normal almost contact $3$-structure.
References:
[1] M. Barros, B. Y. Chen and F. Urbano: Quaternion $CR$-submanifolds of a quaternion manifold. Kodai Math. J. 4 (1981), 399–418. MR 0641361
[2] A. Bejancu: Geometry of $CR$-submanifolds. D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1986. MR 0861408 | Zbl 0605.53001
[3] B. Y. Chen: Geometry of Submanifolds. Marcel Dekker Inc., New York, 1973. MR 0353212 | Zbl 0262.53036
[4] J. Erbacher: Reduction of the codimension of anisometric immersion. J. Differential Geom. 5 (1971), 333–340. DOI 10.4310/jdg/1214429997 | MR 0288701
[5] S. Ishihara: Quaternion Kaehlerian manifolds. J. Differential Geom. 9 (1974), 483–500. DOI 10.4310/jdg/1214432544 | MR 0348687 | Zbl 0297.53014
[6] S. Ishihara and M. Konishi: Differential geometry of fibred spaces. Publication of the Study Group of Geometry, Vol. 8, Institute of Mathematics, Yoshida College, Tokyo, 1973. MR 0405275
[7] D. Krupka: The trace decomposition problem. Beiträge Algebra Geom.; Contrib. Alg. Geom. 36 (1995), 303–315. MR 1358429 | Zbl 0839.15024
[8] Y. Y. Kuo: On almost contact $3$-structure. Tohoku Math. J. 22 (1970), 235–332. MR 0278225 | Zbl 0205.25801
[9] J.-H. Kwon and J. S. Pak: $QR$-submanifolds of $(p-1)$ $QR$-dimension in a quaternionic projective space $QP^{(n+p)/4}$. Acta Math. Hungar. 86 (2000), 89–116. DOI 10.1023/A:1006795518714 | MR 1728592
[10] J.-H. Kwon and J. S. Pak: Scalar curvature of $QR$-submanifolds immersed in a quaternionic projective space. Saitama Math. J 17 (1999), 47–57. MR 1740246
[11] J.-H. Kwon and J. S. Pak: On $n$-dimensional $QR$-submanifolds of $(p-1)$ $QR$-dimension in a quaternionic space form. Preprint.
[12] M. Okumura and L. Vanhecke: A class of normal almost contact $CR$-submanifolds in $C^q$. Rend. Sem. Mat. Univ. Pol. Torino 52 (1994), 359–369. MR 1345606
[13] J. S. Pak: Real hypersurfaces in quaternionic Kaehlerian manifolds with constant $Q$-sectional curvature. Kodai Math. Sem. Rep. 29 (1977), 22–61. DOI 10.2996/kmj/1138833571 | MR 0461384 | Zbl 0424.53012
[14] K. Yano, S. Ishihara and M. Konishi: Normality of almost contact $3$-structure. Tohoku Math. J. 25 (1973), 167–175. DOI 10.2748/tmj/1178241375 | MR 0336644
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