Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Panagiotidou, Konstantina; Pérez, Juan de Dios

doi:10.1515/math-2015-0032

Cited by 8 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [21] we studied the problem of commutativity of Cho operators and shape operator, obtaining that the unique real hypersurfaces in CP m , m ≥ 3, such that F X A = AF X for any X ∈ D are locally congruent to ruled real hypersurfaces. Similar results were obtained in the case of structure Jacobi operator of real hypersurfaces in M n (c), n ≥ 2, (see [22,23]).…”

supporting

confidence: 80%

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

2020

Self Cite

View full text Add to dashboard Cite

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.

show abstract

supporting

confidence: 80%

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lemma 2.1 (cf. [18]) With respect to the standard non-Hopf frame, there are smooth functions κ i (1 ≤ i ≤ 3) such that the following relations hold:…”

Section: The Standard Non-hopf Frame and Their Connectionsmentioning

confidence: 99%

Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in and

Cui¹,

Hu²

2023

Can. Math. Bull.

View full text Add to dashboard Cite

show abstract

“…Almost cosymplectic 3-manifolds and unit tangnet sphere bundles were investigated by the present authors in [19], [20], respectively. Panagiotidou and Xenos investigated real hypersurfaces in complex projective plane and complex hyperbolic plane [28].…”

Section: Introductionmentioning

confidence: 99%

Almost Kenmotsu 3-Manifolds with Pseudo-Parallel Characteristic Jacobi Operator

Lee

Lee²

2022

Results Math

View full text Add to dashboard Cite

In this paper, we treat parallelism of the characteristic Jacobi operator in an almost Kenmotsu 3-manifold. First, we show that there exist no almost Kenmotsu 3-manifolds with vanishing characteristic Jacobi operator. More strongly we show the non-existence of almost Kenmotsu 3-manifolds with parallel characteristic Jacobi operator. On the other hand, we prove that there exists an almost Kenmotsu 3-manifold with η-parallel characteristic Jacobi operator and we find the necessary and sufficient condition for them.Next, we show that almost Kenmotsu 3-manifolds with pseudo-parallel characteristic Jacobi operator are classified into four classes. Moreover, we give a complete classification of all homogeneous almost Kenmotsu 3-manifolds with pseudo-parallel characteristic Jacobi operator.

show abstract

Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Cited by 8 publications

References 4 publications

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in and

Almost Kenmotsu 3-Manifolds with Pseudo-Parallel Characteristic Jacobi Operator

Contact Info

Product

Resources

About