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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Minimal submanifolds in $ℝ^{4}$ with a g.c.K. structure

Marian-Ioan Munteanu (2008)

Czechoslovak Mathematical Journal

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In this paper we obtain all invariant, anti-invariant and $C R$ submanifolds in $(ℝ^{4}, g, J)$ endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.

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

Minimal submanifolds in ℝ 4 with a g.c.K. structure

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 $R^{4 m}$

Minimal submanifolds in $ℝ^{4}$ with a g.c.K. structure