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Bull. Korean Math. Soc. 2014; 51(5): 1375-1397
Printed September 30, 2014
https://doi.org/10.4134/BKMS.2014.51.5.1375
Copyright © The Korean Mathematical Society.
Codimension reduction for submanifolds of unit $(4m+3)$-sphere and its applications
Hyang Sook Kim and Jin Suk Pak
Inje University, Kyungpook National University
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
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