On the normality of an almost contact $3$-structure on $QR$-submanifolds

Shoichi Funabashi; Jin Suk Pak; Yang Jae Shin

Displaying similar documents to “On the normality of an almost contact $3$ -structure on $Q R$ -submanifolds”

On Ricci curvature of totally real submanifolds in a quaternion projective space

Ximin Liu (2002)

Archivum Mathematicum

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Let $M^{n}$ be a Riemannian $n$ -manifold. Denote by $S (p)$ and $\bar{Ric} (p)$ the Ricci tensor and the maximum Ricci curvature on $M^{n}$ , respectively. In this paper we prove that every totally real submanifolds of a quaternion projective space $Q P^{m} (c)$ satisfies $S \leq ((n - 1) c + \frac{n^{2}}{4} H^{2}) g$ , where $H^{2}$ and $g$ are the square mean curvature function and metric tensor on $M^{n}$ , respectively. The equality holds identically if and only if either $M^{n}$ is totally geodesic submanifold or $n = 2$ and $M^{n}$ is totally umbilical submanifold. Also we show that if a Lagrangian submanifold...

A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto, Antonio Lotta (2023)

Archivum Mathematicum

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We prove a Frankel type theorem for $C R$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $C R$ submanifolds of Sasakian space forms.

The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold

Fernando Etayo, Mario Fioravanti, Ujué R. Trías (2001)

Czechoslovak Mathematical Journal

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Let $M$ be a real submanifold of an almost complex manifold $(\bar{M}, \bar{J})$ and let $H_{x} = T_{x} M \cap \bar{J} (T_{x} M)$ be the maximal holomorphic subspace, for each $x \in M$ . We prove that $c M \to ℕ$ , $c (x) = {dim}_{ℝ} H_{x}$ is upper-semicontinuous.

Symmetric twofold CR submanifolds in a Euclidean space $R^{4 m}$

Minoru Kobayashi (1987)

Colloquium Mathematicae

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Displaying similar documents to “On the normality of an almost contact 3 -structure on Q R -submanifolds”

On Ricci curvature of totally real submanifolds in a quaternion projective space

A Frankel type theorem for CR submanifolds of Sasakian manifolds

The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold

Symmetric twofold CR submanifolds in a Euclidean space R 4 m

Displaying similar documents to “On the normality of an almost contact $3$ -structure on $Q R$ -submanifolds”

Symmetric twofold CR submanifolds in a Euclidean space $R^{4 m}$