Displaying similar documents to “Symmetric twofold CR submanifolds in a Euclidean space R 4 m ”

Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

Similarity:

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...

A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto, Antonio Lotta (2023)

Archivum Mathematicum

Similarity:

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.

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

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

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A submanifold M m of a generalized Sasakian-space-form M ¯ 2 n + 1 ( f 1 , f 2 , f 3 ) is said to be C -totally real submanifold if ξ ∈ Γ ( T ⊥ M ) and φ X ∈ Γ ( T ⊥ M ) for all X ∈ 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

Similarity:

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...

The gap theorems for some extremal submanifolds in a unit sphere

Xi Guo and Lan Wu (2015)

Communications in Mathematics

Similarity:

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 ∫ M ρ 2 k d v . In this paper, we can study gap phenomenon for these submanifolds.

f -biminimal maps between Riemannian manifolds

Yan Zhao, Ximin Liu (2019)

Czechoslovak Mathematical Journal

Similarity:

We give the definition of f -biminimal submanifolds and derive the equation for f -biminimal submanifolds. As an application, we give some examples of f -biminimal manifolds. Finally, we consider f -minimal hypersurfaces in the product space ℝ n × 𝕊 1 ( a ) and derive two rigidity theorems.

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

Similarity:

We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds ( M , g M ) and ( B , g B ) in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric g f on M by g f | × ≡ g M | × , g f | × T M ̂ ≡ f ̂ ² g M | × T M ̂ , where and denote the bundles of horizontal and vertical vectors. The manifold ( M , g f ) obtained that way is called a warped submersion. The function f is called a warping function. We show...

On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture

Ze-Jun Hu, Guo-Xin Wei (2003)

Colloquium Mathematicae

Similarity:

Let M̅ be a compact Riemannian manifold with sectional curvature K M ̅ satisfying 1 / 5 < K M ̅ ≤ 1 (resp. 2 ≤ K M ̅ < 10 ), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.