分野別セミナー

概要：
In an $n$-dimensional nonflat complex space form $\widetilde{M}_n(c)
(=\mathbb{C}P^n(c)$ or $\mathbb{C}H^n(c)$),
we classify real hypersurfaces $M^{2n-1}$ which are
Sasakian manifolds with respect to the almost contact metric
structure $(\phi,\xi,\eta,g)$ induced from the K\"ahler structure $J$
and the standard metric $g$ of the ambient space $\widetilde{M}_n(c)$.
Our theorem shows that this Sasakian manifold is a Sasakian space
form $M^{2n-1}(c+1)$ of constant $\phi$-sectional curvature $c+1$
for each $c(\not=0)$.
Each of them is realized as a homogeneous real hypersurface of
$\widetilde{M}_n(c)$. Using this construction of Sasakian space forms,
we investigate the length spectrum of Sasakian space forms in detail.