Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 34, Number 1 (2010), 117-128.
Odd dimensional Riemannian submanifolds admitting the almost contact metric structure in a Euclidean sphere
We investigate some odd dimensional Rimannian submanifolds admitting the almost contact metric structure $(\phi, \xi, \eta, \langle , \rangle)$ of a certain Euclidean sphere from the viewpoint of the weakly $\phi$-invariance of the second fundamental form. The family of such submanifolds contains some homogeneous submanifolds of the ambient sphere. In the latter half of this paper, we caluculate the mean curvature and the length of the derivative of the mean curvature vector of these homogeneous submanifolds.
Tsukuba J. Math., Volume 34, Number 1 (2010), 117-128.
First available in Project Euclid: 8 September 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
real hypersurfaces complex projective spaces real hypersurfaces of type (A) Hopf hypersurfaces ruled real hypersurfaces homogeneous submanifold strongly $\phi$-invariant weakly $\phi$-invariant the first standard minimal embedding Euclidean spheres mean curvature vector length of the mean curvature vector
Kazuhiro, Okumura. Odd dimensional Riemannian submanifolds admitting the almost contact metric structure in a Euclidean sphere. Tsukuba J. Math. 34 (2010), no. 1, 117--128. doi:10.21099/tkbjm/1283967411. https://projecteuclid.org/euclid.tkbjm/1283967411