scholarly journals A `xi`-projectively flat connection on Kenmotsu manifolds

2020 ◽  
Vol 1 (1) ◽  
pp. 0-0
Author(s):  
Vahid Pirhadi ◽  
Keyword(s):  
Flat Connection ◽  
Projectively Flat ◽  
Kenmotsu Manifolds

scholarly journals GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS

2011 ◽  
Vol 90 (2) ◽  
pp. 221-235 ◽  
Author(s):  
SIYE WU
Keyword(s):  
Hilbert Spaces ◽  
Maslov Index ◽  
Harmonic Oscillators ◽  
Complex Structures ◽  
Flat Connection ◽  
Geometric Phases ◽  
Berry's Phase ◽  
Geometric Quantisation ◽  
Projectively Flat ◽  
Fermionic Systems

AbstractAfter reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.

scholarly journals Certain results on Lorentzian para-Kenmotsu manifolds

2021 ◽  
Vol 39 (3) ◽  
pp. 201-220
Author(s):  
Abdul Haseeb ◽  
Rajendra Prasad
Keyword(s):  
Einstein Manifold ◽  
Conformally Flat ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The object of the present paper is to study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection satisfying the conditions $\bar R\cdot \bar S=0$ and $\bar S\cdot \bar R=0$. After that we study $\phi$-conformally flat, $\phi$-conharmonically flat, $\phi$-concircularly flat, $\phi$-projectively flat and conformally flat Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and it is shown that in each of these case the manifold is generalized $\eta$-Einstein manifold.

scholarly journals f-Kenmotsu manifolds with the Schouten-van Kampen connection

2017 ◽  
Vol 102 (116) ◽  
pp. 93-105 ◽  
Author(s):  
Ahmet Yıldız
Keyword(s):  
3 Dimensional ◽  
Projectively Flat ◽  
Kenmotsu Manifolds

We study 3-dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection. With the help of such a connection, we study projectively flat, conharmonically flat, Ricci semisymmetric and semisymmetric 3-dimensional f-Kenmotsu manifolds. Finally, we give an example of 3- dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection.

η-Einstein nearly Kenmotsu manifolds

2019 ◽  
Vol 12 (06) ◽  
pp. 2040010 ◽  
Author(s):  
Pelin Tekin ◽  
Nesip Aktan
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Kenmotsu Manifold ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Projective Curvature ◽  
Conharmonic Curvature Tensor ◽  
Projective Curvature Tensor ◽  
Tensor Formula

In this paper, we showed that an [Formula: see text]-Einstein nearly Kenmotsu manifold with projective curvature tensor [Formula: see text], and conharmonic curvature tensor [Formula: see text], satisfy the conditions [Formula: see text] and [Formula: see text], respectively. Furthermore, we obtain scalar curvature of a projectively flat and a conharmonically flat [Formula: see text]-Einstein nearly Kenmotsu manifold.

scholarly journals Semi-Symmetric Metric Connection on Homothetic Kenmotsu Manifolds

2020 ◽  
Vol 12 (3) ◽  
pp. 223-232
Author(s):  
L. Thangmawia ◽  
R. Kumar
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The object of the paper is to study homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. We discuss locally -symmetric homothetic Kenmotsu manifold and -projectively flat homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we construct an example of 3-dimensional homothetic Kenmotsu manifold to verify some results.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

On Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection

2018 ◽  
Vol 48 (1) ◽  
pp. 47-60
Author(s):  
Pradip Majhi ◽  
Ajit Barman ◽  
Uday Chand De
Keyword(s):  
Kenmotsu Manifolds
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