|
Fundamentalnaya i Prikladnaya Matematika, 2002, Volume 8, Issue 2, Pages 357–364
(Mi fpm650)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
On the type number of nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds
M. B. Banaru Moscow State Pedagogical University
Abstract:
Nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds are considered. The following results are obtained.
Theorem 1.
The type number of a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold is at most one.
Theorem 2.
Let $\sigma$ be the second fundamental form of the immersion of a nearly-cosymplectic hypersurface $(N,\{\Phi,\xi,\eta,g\})$ in a nearly-Kählerian manifold $M^{2n}$. Then $N$ is a minimal submanifold of $M^{2n}$ if and only if $\sigma(\xi,\xi)=0$.
Theorem 3.
Let $N$ be a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold $M^{2n}$, and let $T$ be its type number. Then the following statements are equivalent: 1) $N$ is a minimal submanifold of $M^{2n}$; 2) $N$ is a totally geodesic submanifold of $M^{2n}$; 3) $T\equiv0$.
Received: 01.03.2002
Citation:
M. B. Banaru, “On the type number of nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds”, Fundam. Prikl. Mat., 8:2 (2002), 357–364
Linking options:
https://www.mathnet.ru/eng/fpm650 https://www.mathnet.ru/eng/fpm/v8/i2/p357
|
Statistics & downloads: |
Abstract page: | 430 | Full-text PDF : | 134 | References: | 56 | First page: | 2 |
|