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.
Publié le : 2010-08-15
Classification:
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,
53B25,
53C40
@article{1283967411,
author = {Kazuhiro, Okumura},
title = {Odd dimensional Riemannian submanifolds admitting the almost
contact metric structure in a Euclidean sphere},
journal = {Tsukuba J. Math.},
volume = {34},
number = {1},
year = {2010},
pages = { 117-128},
language = {en},
url = {http://dml.mathdoc.fr/item/1283967411}
}
Kazuhiro, Okumura. Odd dimensional Riemannian submanifolds admitting the almost
contact metric structure in a Euclidean sphere. Tsukuba J. Math., Tome 34 (2010) no. 1, pp. 117-128. http://gdmltest.u-ga.fr/item/1283967411/