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 Codimension reduction for submanifolds of unit $(4m+3)$-sphere and its applications Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1375-1397 https://doi.org/10.4134/BKMS.2014.51.5.1375Printed September 30, 2014 Hyang Sook Kim and Jin Suk Pak Inje University, Kyungpook National University Abstract : In this paper we establish codimension reduction theorem for submanifolds of a $(4m+3)$-dimensional unit sphere $S^{4m+3}$ with Sasakian 3-structure and apply it to submanifolds of a quaternionic projective space. Keywords : codimension reduction, unit $(4m+3)$-sphere, Sasakian $3$-structure, normal connection, quaternionic projective space, $L$-flat, mean curvature vector, totally geodesic MSC numbers : 53C40, 53C25 Downloads: Full-text PDF