Tsukuba Journal of Mathematics

Odd dimensional Riemannian submanifolds admitting the almost contact metric structure in a Euclidean sphere

Okumura Kazuhiro

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Abstract

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.

Article information

Source
Tsukuba J. Math., Volume 34, Number 1 (2010), 117-128.

Dates
First available in Project Euclid: 8 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1283967411

Digital Object Identifier
doi:10.21099/tkbjm/1283967411

Mathematical Reviews number (MathSciNet)
MR2723727

Zentralblatt MATH identifier
1198.53016

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C40: Global submanifolds [See also 53B25]

Keywords
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

Citation

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


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