scholarly journals The canonical foliation of a compact generalized Hopf manifold

1999 ◽  
Vol 11 (1) ◽  
pp. 13-28 ◽  
Author(s):  
Kazumi Tsukada
Keyword(s):  
Canonical Foliation ◽  
Hopf Manifold

scholarly journals On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 333
Author(s):  
Elisabetta Barletta ◽  
Sorin Dragomir ◽  
Francesco Esposito
Keyword(s):  
Decomposition Theorem ◽  
Conformally Flat ◽  
Canonical Foliation ◽  
Locally Conformal Kähler ◽  
De Rham ◽  
Vaisman Manifold ◽  
Geodesically Complete ◽  
Locally Conformal ◽  
Lee Form ◽  
Hopf Manifold

We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature c/4, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vaisman manifold of index 2s, 0<s<n, is locally biholomorphically homothetic to an indefinite complex Hopf manifold CHsn(λ), 0<λ<1, equipped with the indefinite Boothby metric gs,n.

scholarly journals Unstable harmonic maps into real hypersurfaces of a complex Hopf manifold

2001 ◽  
Vol 25 (1) ◽  
pp. 203-213
Author(s):  
Sorin Dragomir ◽  
Maria Rosaria Enea
Keyword(s):  
Harmonic Maps ◽  
Real Hypersurfaces ◽  
Hopf Manifold

scholarly journals Dolbeault cohomology of complex manifolds with torus action

2021 ◽  
pp. 173-187
Author(s):  
Roman Krutowski ◽  
Taras Panov
Keyword(s):  
Symmetry Group ◽  
Blow Up ◽  
Hodge Decomposition ◽  
Torus Action ◽  
Cohomology Algebra ◽  
Complex Manifolds ◽  
Dolbeault Cohomology ◽  
Canonical Foliation

We describe the basic Dolbeault cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a DGA model for the ordinary Dolbeault cohomology algebra. The Hodge decomposition for the basic Dolbeault cohomology is proved by reducing to the transversely Kähler (equivalently, polytopal) case using a foliated analogue of toric blow-up.

Left-invariant almost α-coKähler structures on 3D semidirect product Lie groups

2019 ◽  
Vol 16 (01) ◽  
pp. 1950011 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Lie Groups ◽  
Semidirect Product ◽  
Three Dimensional ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
The Matrix ◽  
Canonical Foliation ◽  
Matrix Formula ◽  
Simply Connected

The main result of this paper gives a characterization of left-invariant almost [Formula: see text]-coKähler structures on three-dimensional (3D) semidirect product Lie groups [Formula: see text] in terms of the matrix [Formula: see text]. Then, we study the harmonicity of the Reeb vector field [Formula: see text] of a simply connected homogeneous almost [Formula: see text]-coKähler three-manifold, in terms of the Gaussian curvature of the canonical foliation.

scholarly journals Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ntokozo Sibonelo Khuzwayo ◽  
Fortuné Massamba
Keyword(s):  
Vector Field ◽  
Curvature Vector ◽  
Almost Kähler Manifold ◽  
Canonical Foliation ◽  
Almost Kähler ◽  
The Mean ◽  
Curvature Tensors ◽  
Locally Conformal ◽  
Kähler Structures ◽  
Almost Kähler Structures

We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

scholarly journals Generalized Quasi-Einstein Manifolds in Contact Geometry

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1592
Author(s):  
İnan Ünal
Keyword(s):  
Constant Curvature ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Contact Pair ◽  
Einstein Manifolds ◽  
Cyclic Parallel Ricci Tensor ◽  
Codazzi Type ◽  
Curvature Tensors ◽  
Parallel Ricci Tensor ◽  
Hopf Manifold

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.

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