scholarly journals OnV-Killing forms in a locally conformal Kähler manifold with the parallel lee form

1979 ◽  
Vol 121 (1) ◽  
pp. 387-396
Author(s):  
Toyoko Kashiwada
Keyword(s):  
Kähler Manifold ◽  
Kahler Manifold ◽  
Locally Conformal Kähler ◽  
Locally Conformal ◽  
Lee Form

scholarly journals On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

1995 ◽  
Vol 18 (2) ◽  
pp. 331-340
Author(s):  
M. Hasan shahid ◽  
A. Sharfuddin
Keyword(s):  
Necessary Conditions ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kahler Manifold ◽  
Generic Submanifolds ◽  
Locally Conformal Kähler ◽  
Generic Submanifold ◽  
Locally Conformal ◽  
Totally Real

The study ofCR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted byP,F,tandf, to have parallelP,Fandt. We also prove that for a generic submanifold of a locally conformal Kähler manifold,Fis parallel ifftis parallel.

A NOTE ON THE MORSE–NOVIKOV COHOMOLOGY OF BLOW-UPS OF LOCALLY CONFORMAL KÄHLER MANIFOLDS

2014 ◽  
Vol 91 (1) ◽  
pp. 155-166 ◽  
Author(s):  
XIANGDONG YANG ◽  
GUOSONG ZHAO
Keyword(s):  
Blow Up ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kahler Manifold ◽  
Locally Conformal Kähler ◽  
Locally Conformal

AbstractWe prove a blow-up formula for Morse–Novikov cohomology on a compact locally conformal Kähler manifold.

scholarly journals The Concircular Curvature Tensor Of The Locally Conformal Kahler Manifold

2019 ◽  
Vol 24 (7) ◽  
pp. 110
Author(s):  
Ali Abdalmajed. Shihab1 ◽  
Dheyaa Nathim Ahmed2
Keyword(s):  
Curvature Tensor ◽  
Kähler Manifold ◽  
Riemannian Curvature ◽  
Classical Symmetry ◽  
Kahler Manifold ◽  
Symmetry Properties ◽  
Conharmonic Curvature Tensor ◽  
Locally Conformal Kähler ◽  
Concircular Curvature Tensor ◽  
Locally Conformal

In this research, we are calculated components conharmonic curvature tensor in some aspects Hermeation manifolding in particular of the Locally Conformal Kahler manifold. And we prove that this tensor possesses the classical symmetry properties of the Riemannian curvature. They also, establish relationships between the components of the tensor in this manifold   http://dx.doi.org/10.25130/tjps.24.2019.137

HEISENBERG, SPHERICAL CR-GEOMETRY AND BOCHNER FLAT LOCALLY CONFORMAL KÄHLER MANIFOLDS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1089-1116
Author(s):  
YOSHINOBU KAMISHIMA
Keyword(s):  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Cr Geometry ◽  
Survey Article ◽  
Kahler Manifold ◽  
Locally Conformal Kähler ◽  
Spherical Cr Manifolds ◽  
Locally Conformal ◽  
The Relationship

This is a survey article for the relationship between spherical CR-manifolds and Bochner flat Kähler manifolds. We shall give a uniformization of Bochner flat Kähler manifolds. A Bochner flat locally conformal Kähler manifold is a locally conformal Kähler manifold with vanishing Bochner curvature tensor. We shall apply our result to Bochner flat locally conformal Kähler manifolds.

scholarly journals Example of a six-dimensional LCK solvmanifold

2017 ◽  
Vol 4 (1) ◽  
pp. 37-42
Author(s):  
Hiroshi Sawai
Keyword(s):  
Lie Group ◽  
Locally Conformal Kähler ◽  
Locally Conformal ◽  
Lee Form ◽  
Solvable Lie Group

Abstract The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.

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.

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