A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto; Antonio Lotta

Displaying similar documents to “A Frankel type theorem for CR submanifolds of Sasakian manifolds”

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

Minoru Kobayashi (1987)

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Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Payel Karmakar (2024)

Mathematica Bohemica

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We study totally contact umbilical screen-slant lightlike submanifolds and totally contact umbilical screen-transversal lightlike submanifolds of an indefinite Kenmotsu manifold. We prove a characterization theorem of totally contact umbilical screen-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We further prove some results on a totally contact umbilical radical screen-transversal lightlike submanifold of an indefinite Kenmotsu manifold, such as the necessary and...

Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

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We define a $C^{1}$ distance between submanifolds of a riemannian manifold $M$ and show that, if a compact submanifold $N$ is not moved too much under the isometric action of a compact group $G$ , there is a $G$ -invariant submanifold $C^{1}$ -close to $N$ . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros...

On minimal generic submanifolds immersed in $S^{2 m + 1}$

Masahiro Kon (2001)

Colloquium Mathematicae

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We give a pinching theorem for a compact minimal generic submanifold with flat normal connection immersed in an odd-dimensional sphere with standard Sasakian structure.

Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Shyamal K. Hui, Richard S. Lemence, Pradip Mandal (2020)

Commentationes Mathematicae Universitatis Carolinae

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A submanifold $M^{m}$ of a generalized Sasakian-space-form ${\bar{M}}^{2 n + 1} (f_{1}, f_{2}, f_{3})$ is said to be $C$ -totally real submanifold if $ξ \in Γ (T^{⊥} M)$ and $φ X \in Γ (T^{⊥} M)$ for all $X \in Γ (T M)$ . In particular, if $m = n$ , then $M^{n}$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.

Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space

Weiller F. C. Barboza, H. F. de Lima, M. A. Velásquez (2023)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we deal with $n$ -dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_{p}^{n + p}$ of index $p > 1$ , which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric...

A characterization of a minimal submanifold in $R^{n + p}$

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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...

The gap theorems for some extremal submanifolds in a unit sphere

Xi Guo and Lan Wu (2015)

Communications in Mathematics

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Let $M$ be an $n$ -dimensional submanifold in the unit sphere $S^{n + p}$ , we call $M$ a $k$ -extremal submanifold if it is a critical point of the functional $\int_{M} ρ^{2 k} d v$ . In this paper, we can study gap phenomenon for these submanifolds.

Projective Curvature Tensorin 3-dimensional Connected Trans-Sasakian Manifolds

Krishnendu De, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study $ξ$ -projectively flat and $φ$ -projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.

Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar (2022)

Mathematica Bohemica

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The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $ξ$ -projectively flat, $M$ -projectively flat, $ξ$ - $M$ -projectively flat, pseudo projectively flat and $ξ$ -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on...